On P-adic Differential Equations on Semistable Varieties
Author | : Valentina Di Proietto |
Publisher | : |
Total Pages | : |
Release | : 2009 |
Genre | : |
ISBN | : |
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Author | : Valentina Di Proietto |
Publisher | : |
Total Pages | : |
Release | : 2009 |
Genre | : |
ISBN | : |
Author | : Kiran S. Kedlaya |
Publisher | : Cambridge University Press |
Total Pages | : 399 |
Release | : 2010-06-10 |
Genre | : Mathematics |
ISBN | : 1139489208 |
Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
Author | : Kiran Sridhara Kedlaya |
Publisher | : |
Total Pages | : 400 |
Release | : 2014-05-14 |
Genre | : Mathematics |
ISBN | : 9780511750182 |
The first comprehensive, unified development of the theory of p-adic differential equations.
Author | : Glenn Stevens |
Publisher | : American Mathematical Soc. |
Total Pages | : 334 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 0821851802 |
The workshop aimed to deepen understanding of the interdependence between p-adic Hodge theory, analogues of the conjecture of Birch and Swinnerton-Dyer, p-adic uniformization theory, p-adic differential equations, and deformations of Gaels representations.
Author | : John Cremona |
Publisher | : Birkhäuser |
Total Pages | : 291 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034879199 |
This book presents lectures from a conference on "Modular Curves and Abelian Varieties'' at the Centre de Recerca Matemtica (Bellaterra, Barcelona). The articles in this volume present the latest achievements in this extremely active field and will be of interest both to specialists and to students and researchers. Many contributions focus on generalizations of the Shimura-Taniyama conjecture to varieties such as elliptic Q-curves and Abelian varieties of GL_2-type. The book also includes several key articles in the subject that do not correspond to conference lectures.
Author | : |
Publisher | : World Scientific |
Total Pages | : 1191 |
Release | : |
Genre | : |
ISBN | : |
Author | : Yves André |
Publisher | : Birkhäuser |
Total Pages | : 223 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034883366 |
"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables." --Mathematical Reviews
Author | : Bruno Chiarellotto |
Publisher | : American Mathematical Society |
Total Pages | : 124 |
Release | : 2023-09-15 |
Genre | : Mathematics |
ISBN | : 1470467062 |
View the abstract.
Author | : Reinhardt Kiehl |
Publisher | : Springer Science & Business Media |
Total Pages | : 382 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662045761 |
The authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.
Author | : Ahmed Abbes |
Publisher | : Springer Nature |
Total Pages | : 450 |
Release | : 2024 |
Genre | : Hodge theory |
ISBN | : 3031559142 |
This book delves into the p-adic Simpson correspondence, its construction, and development. Offering fresh and innovative perspectives on this important topic in algebraic geometry, the text serves a dual purpose: it describes an important tool in p-adic Hodge theory, which has recently attracted significant interest, and also provides a comprehensive resource for researchers. Unique among the books in the existing literature in this field, it combines theoretical advances, novel constructions, and connections to Hodge-Tate local systems. This exposition builds upon the foundation laid by Faltings, the collaborative efforts of the two authors with T. Tsuji, and contributions from other researchers. Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence, whose construction has been taken up in several different ways. Following the approach they initiated with T. Tsuji, the authors develop new features of the p-adic Simpson correspondence, inspired by their construction of the relative Hodge-Tate spectral sequence. First, they address the connection to Hodge-Tate local systems. Then they establish the functoriality of the p-adic Simpson correspondence by proper direct image. Along the way, they expand the scope of their original construction. The book targets a specialist audience interested in the intricate world of p-adic Hodge theory and its applications, algebraic geometry and related areas. Graduate students can use it as a reference or for in-depth study. Mathematicians exploring connections between complex and p-adic geometry will also find it valuable. .