Download or read book Degenerating Curves and Their Jacobians written by Dino Jacques Lorenzini and published by . This book was released on 1988 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rigid Geometry of Curves and Their Jacobians written by Werner Lütkebohmert and published by Springer. This book was released on 2016-01-26 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Download or read book Curves and Their Jacobians written by David Mumford and published by Ann Arbor : University of Michigan Press, c1975, 1976 printing.. This book was released on 1975 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Geometry III written by A.N. Parshin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.
Download or read book Curves Jacobians and Abelian Varieties written by Ron Donagi and published by American Mathematical Soc.. This book was released on 1992 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on the Schottky Problem, held in June 1990 at the University of Massachusetts at Amherst. The conference explored various aspects of the Schottky problem of characterizing Jacobians of curves among all abelian varieties. Some of the articles study related themes, including the moduli of stable vector bundles on a curve. Prym varieties and intermediate Jacobians, and special Jacobians with exotic polarizations or product structures.
Download or read book Lectures on Algebraic Geometry II written by Günter Harder and published by Springer Science & Business Media. This book was released on 2011-04-21 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.
Download or read book N ron Models written by Siegfried Bosch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Néron models were invented by A. Néron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of Néron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Néron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of Néron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Néron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Néron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.
Download or read book Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields written by Lisa Berger and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.
Download or read book Jacobians of Shimura Curves and Jacquet Langlands Correspondences written by David Frederick Helm and published by . This book was released on 2003 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Celebration of Algebraic Geometry written by Brendan Hassett and published by American Mathematical Soc.. This book was released on 2013-09-11 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
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 The Red Book of Varieties and Schemes written by David Mumford and published by Springer. This book was released on 2004-02-24 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
Download or read book An Introduction to the Langlands Program written by Joseph Bernstein and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
Download or read book Curves and Abelian Varieties written by Valery Alexeev and published by American Mathematical Soc.. This book was released on 2008 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes." "In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors. of compactified Jucobiuns of singular curves, and of "strange duality" among moduli spaces of vector bundles on algebraic varieties."--BOOK JACKET.
Download or read book Mathematical Aspects of Computer and Information Sciences written by Johannes Blömer and published by Springer. This book was released on 2017-12-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017, held in Vienna, Austria, in November 2017. The 28 revised papers and 8 short papers presented were carefully reviewed and selected from 67 submissions. The papers are organized in the following topical sections: foundation of algorithms in mathematics, engineering and scientific computation; combinatorics and codes in computer science; data modeling and analysis; and mathematical aspects of information security and cryptography.
Download or read book K3 Surfaces and Their Moduli written by Carel Faber and published by Birkhäuser. This book was released on 2016-04-22 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like “The Moduli Space of Curves” and “Moduli of Abelian Varieties,” which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics. K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry. Contributors: S. Boissière, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.
Download or read book Index to American Doctoral Dissertations written by and published by . This book was released on 1989 with total page 1252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
