Download or read book Arithmetic Fundamental Groups and Noncommutative Algebra written by Michael D. Fried and published by American Mathematical Soc.. This book was released on 2002 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G {\mathbb Q $ of the algebraic numbers and its close relatives. By analyzing how $G {\mathbb Q $ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s. Papers in Part 2 apply $\theta$-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map. This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.
Download or read book Non abelian Fundamental Groups and Iwasawa Theory written by John Coates and published by Cambridge University Press. This book was released on 2011-12-15 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the interaction between several key aspects of Galois theory based on Iwasawa theory, fundamental groups and automorphic forms. These ideas encompass a large portion of mainstream number theory and ramifications that are of interest to graduate students and researchers in number theory, algebraic geometry, topology and physics.
Download or read book The Arithmetic of Fundamental Groups written by Jakob Stix and published by Springer Science & Business Media. This book was released on 2012-01-10 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its analogies have found numerous applications in mathematics that are still being investigated today, and which are explored in this volume, the result of a meeting at Heidelberg University that brought together mathematicians who use or study fundamental groups in their work with an eye towards applications in arithmetic. The book acknowledges the varied incarnations of the fundamental group: pro-finite, l-adic, p-adic, pro-algebraic and motivic. It explores a wealth of topics that range from anabelian geometry (in particular the section conjecture), the l-adic polylogarithm, gonality questions of modular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's non-abelian Chabauty method and p-adic integration after Coleman. The editor has also included the abstracts of all the talks given at the Heidelberg meeting, as well as the notes on Coleman integration and on Grothendieck's fundamental group with a view towards anabelian geometry taken from a series of introductory lectures given by Amnon Besser and Tamás Szamuely, respectively.
Download or read book Galois Groups and Fundamental Groups written by Leila Schneps and published by Cambridge University Press. This book was released on 2003-07-21 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Download or read book Galois Groups and Fundamental Groups written by Tamás Szamuely and published by Cambridge University Press. This book was released on 2009-07-16 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.
Download or read book Groups Combinatorics Geometry written by A. A. Ivanov and published by World Scientific. This book was released on 2003 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book contains the proceedings of the L.M.S. Durham Symposium on Groups, Geometry and Combinatorics, July 16-26, 2001"--P. v.
Download or read book Algebra Arithmetic and Geometry with Applications written by Chris Christensen and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Conference on Algebra and Algebraic Geometry with Applications, July 19 – 26, 2000, at Purdue University to honor Professor Shreeram S. Abhyankar on the occasion of his seventieth birthday. Eighty-five of Professor Abhyankar's students, collaborators, and colleagues were invited participants. Sixty participants presented papers related to Professor Abhyankar's broad areas of mathematical interest. Sessions were held on algebraic geometry, singularities, group theory, Galois theory, combinatorics, Drinfield modules, affine geometry, and the Jacobian problem. This volume offers an outstanding collection of papers by expert authors.
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Download or read book Algebraic Geometry and Number Theory written by Hussein Mourtada and published by Birkhäuser. This book was released on 2017-05-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Download or read book Computational Algebraic and Analytic Geometry written by Mika Seppälä and published by American Mathematical Soc.. This book was released on 2012 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of three AMS Special Sessions on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties held January 8, 2007, in New Orleans, LA; January 6, 2009, in Washington, DC; and January 6, 2011, in New Orleans, LA. Algebraic, analytic, and geometric methods are used to study algebraic curves and Riemann surfaces from a variety of points of view. The object of the study is the same. The methods are different. The fact that a multitude of methods, stemming from very different mathematical cultures, can be used to study the same objects makes this area both fascinating and challenging.
Download or read book Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I Generic Covers and Covers with Many Branch Points written by Robert M. Guralnick and published by American Mathematical Soc.. This book was released on 2007 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. The authors show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$.
Download or read book Algebraic Groups and Arithmetic written by S. G. Dani and published by Narosa Publishing House. This book was released on 2004 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Major advances have been made in recent decades in algebraic groups and arithmetic. The School of Mathematics of the Tata Institute of Fundamental Research, under the leadership of Professor M. S. Raghunathan, has been a significant contributor to this progress. This collection of papers grew out of a conference held in honor of Professor Raghunathan's sixtieth birthday. The volume contains original papers contributed by leading experts. Topics covered include group-theoretic aspects, Diophantine approximation, modular forms, representation theory, interactions with topology and geometry, and dynamics on homogeneous spaces. Particularly noteworthy are two expository articles on Professor Raghunathan's work by the late Armand Borel and Gopal Prasad. The book is suitable for graduate students and researchers interested in algebra and algebraic geometry.
Download or read book Iwasawa Theory 2012 written by Thanasis Bouganis and published by Springer. This book was released on 2014-12-08 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).
Download or read book Progress in Galois Theory written by Helmut Voelklein and published by Springer Science & Business Media. This book was released on 2006-08-10 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory'). What are the implica tions for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).
Download or read book Automorphic Forms and Zeta Functions written by Siegfried Bcherer and published by World Scientific. This book was released on 2006 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L -functions, many of which are closely related to Arakawa''s works. This collection of papers illustrates Arakawa''s contributions and the current trends in modular forms in several variables and related zeta functions. Contents: Tsuneo Arakawa and His Works; Estimate of the Dimensions of Hilbert Modular Forms by Means of Differential Operators (H Aoki); MarsdenOCoWeinstein Reduction, Orbits and Representations of the Jacobi Group (R Berndt); On Eisenstein Series of Degree Two for Squarefree Levels and the Genus Version of the Basis Problem I (S BAcherer); Double Zeta Values and Modular Forms (H Gangl et al.); Type Numbers and Linear Relations of Theta Series for Some General Orders of Quaternion Algebras (K-I Hashimoto); Skew-Holomorphic Jacobi Forms of Higher Degree (S Hayashida); A Hermitian Analog of the Schottky Form (M Hentschel & A Krieg); The Siegel Series and Spherical Functions on O (2 n) / (O (n) x O (n) ) (Y Hironaka & F Sato); KoecherOCoMaa Series for Real Analytic Siegel Eisenstein Series (T Ibukiyama & H Katsurada); A Short History on Investigation of the Special Values of Zeta and L -Functions of Totally Real Number Fields (T Ishii & T Oda); Genus Theta Series, Hecke Operators and the Basis Problem for Eisenstein Series (H Katsurada & R Schulze-Pillot); The Quadratic Mean of Automorphic L -Functions (W Kohnen et al.); Inner Product Formula for Kudla Lift (A Murase & T Sugano); On Certain Automorphic Forms of Sp (1, q ) (Arakawa''s Results and Recent Progress) (H-A Narita); On Modular Forms for the Paramodular Groups (B Roberts & R Schmidt); SL(2, Z)-Invariant Spaces Spanned by Modular Units (N-P Skoruppa & W Eholzer). Readership: Researchers and graduate students in number theory or representation theory as well as in mathematical physics or combinatorics."
Download or read book Automorphic Forms And Zeta Functions Proceedings Of The Conference In Memory Of Tsuneo Arakawa written by Masanobu Kaneko and published by World Scientific. This book was released on 2006-01-03 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L-functions, many of which are closely related to Arakawa's works.This collection of papers illustrates Arakawa's contributions and the current trends in modular forms in several variables and related zeta functions.
