Download or read book EXCURSION INTO P ADIC HODGE THEORY written by and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book P adic Heights and P adic Hodge Theory written by Denis Benois and published by . This book was released on 2020 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book p adic Hodge Theory Singular Varieties and Non Abelian Aspects written by Bhargav Bhatt and published by Springer Nature. This book was released on 2023-03-28 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning non-abelian aspects This volume contains both original research articles as well as articles that contain both new research as well as survey some of these recent developments.
Download or read book Integral P adic Hodge Theory written by Christophe Breuil and published by . This book was released on 2001 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Relative p adic hodge theory written by Kiran Sridhara Kedlaya and published by . This book was released on 2015 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Towards Non Abelian p adic Hodge Theory in the Good Reduction Case written by Martin C. Olsson and published by American Mathematical Soc.. This book was released on 2011 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Berkeley Lectures on P adic Geometry written by Peter Scholze and published by Princeton University Press. This book was released on 2020-05-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
Download or read book Arithmetic and Geometry written by Gisbert Wüstholz and published by Princeton University Press. This book was released on 2019-10-08 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria—provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces. The second course, taught by Umberto Zannier, addresses the famous Pell equation—not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course, taught by Shou-Wu Zhang, originates in the Chowla–Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross–Zagier formula on Shimura curves and verify the Colmez conjecture on average.
Download or read book Automorphic Forms and Galois Representations written by Fred Diamond and published by Cambridge University Press. This book was released on 2014-10-16 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
Download or read book Automorphic Forms and Galois Representations Volume 2 written by Fred Diamond and published by Cambridge University Press. This book was released on 2014-10-16 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume two include curves and vector bundles in p-adic Hodge theory, associators, Shimura varieties, the birational section conjecture, and other topics of contemporary interest.
Download or read book P adic Hodge Theory in Rigid Analytic Families written by Rebecca Michal Bellovin and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study p-adic Hodge theory in rigid analytic families. Roughly speaking, p-adic Hodge theory is the study of p-adic representations of p-adic Galois groups. One introduces certain p-adic period rings B, such as B_{HT}, B_{dR}, B_{st}, and B_{cris}, and uses them to define functors D_B(.) from the category of p-adic Galois representations to various categories of linear algebra data. In the first half of this thesis, we study generalizations of these functors to families of p-adic Galois representations with rigid analytic coefficients. We prove that the functors D_{HT}(.) and D_{dR}(.) are coherent sheaves, and we prove that the B-admissible locus is a closed subspace of the base. In the second half of this thesis, we study the linear algebra data which arises from families of potentially semi-stable Galois representations valued in a connected reductive group G. We prove that for any G, the moduli space of linear algebra data is reduced and locally a complete intersection, and we deduce that potentially semi-stable deformation rings are generically smooth and equi-dimensional.
Download or read book Period Domains over Finite and p adic Fields written by Jean-François Dat and published by Cambridge University Press. This book was released on 2010-07-08 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is, on the one hand, a pedagogical introduction to the formalism of slopes, of semi-stability and of related concepts in the simplest possible context. It is therefore accessible to any graduate student with a basic knowledge in algebraic geometry and algebraic groups. On the other hand, the book also provides a thorough introduction to the basics of period domains, as they appear in the geometric approach to local Langlands correspondences and in the recent conjectural p-adic local Langlands program. The authors provide numerous worked examples and establish many connections to topics in the general area of algebraic groups over finite and local fields. In addition, the end of each section includes remarks on open questions, historical context and references to the literature.
Download or read book Cyclic Cohomology at 40 Achievements and Future Prospects written by A. Connes and published by American Mathematical Society. This book was released on 2023-02-23 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27–October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.
Download or read book Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Download or read book Supersingular P adic L functions Maass Shimura Operators and Waldspurger Formulas written by Daniel Kriz and published by Princeton University Press. This book was released on 2021-11-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.
Download or read book Integral P adic Hodge Theory of Formal Schemes in Low Ramification written by Yu Min (auteur d'une thèse en Mathématiques).) and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that for any proper smooth formal scheme X over OK, where OK is the ring of integers in a complete discretely valued nonarchimedean extension K of Qp with perfect residue field k and ramification degree e, the i-th Breuil-Kisin cohomology group and its Hodge-Tate specialization admit nice decompositions when ie
Download or read book Hodge Theory and Complex Algebraic Geometry I written by Claire Voisin and published by Cambridge University Press. This book was released on 2007-12-20 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.
