P-adic Vector Bundles on Curves and Abelian Varieties and Representations of the Fundamental Group
Author : Thomas Ludsteck
Publisher :
Page : 0 pages
File Size : 33,75 MB
Release : 2008
Category :
ISBN :
Author : Thomas Ludsteck
Publisher :
Page : 0 pages
File Size : 33,75 MB
Release : 2008
Category :
ISBN :
Author : Kang Zuo
Publisher : Springer
Page : 142 pages
File Size : 18,4 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540484248
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 203 pages
File Size : 40,37 MB
Release : 1997-11-15
Category : Mathematics
ISBN : 1439863865
This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Author : David J. Benson
Publisher : Cambridge University Press
Page : 347 pages
File Size : 45,59 MB
Release : 2017
Category : Mathematics
ISBN : 1107174171
An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.
Author : Valery Alexeev
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 49,96 MB
Release : 2008
Category : Mathematics
ISBN : 0821843346
"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.
Author : Eng-chye Tan
Publisher : World Scientific
Page : 426 pages
File Size : 38,58 MB
Release : 2004
Category : Science
ISBN : 981238779X
The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on ?Representation Theory of Lie Groups? from July 2002 to January 2003. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.This invaluable volume collects the expanded lecture notes of those tutorials. The topics covered include uncertainty principles for locally compact abelian groups, fundamentals of representations of p-adic groups, the Harish-Chandra-Howe local character expansion, classification of the square-integrable representations modulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur-Weyl-Howe duality.The lecturers include Tomasz Przebinda from the University of Oklahoma, USA; Gordan Savin from the University of Utah, USA; Stephen DeBacker from Harvard University, USA; Marko Tadi? from the University of Zagreb, Croatia; Jing-Song Huang from The Hong Kong University of Science and Technology, Hong Kong; Pavle Pand?i? from the University of Zagreb, Croatia; Chal Benson and Gail Ratcliff from East Carolina University, USA; and Roe Goodman from Rutgers University, USA.
Author : Moshe Jarden
Publisher : American Mathematical Soc.
Page : 200 pages
File Size : 44,58 MB
Release : 2021-05-03
Category : Education
ISBN : 1470452073
This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.
Author : Jakob Stix
Publisher : Springer Science & Business Media
Page : 387 pages
File Size : 12,95 MB
Release : 2012-01-10
Category : Mathematics
ISBN : 3642239056
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.
Author : Vijaya Kumar Murty
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 13,70 MB
Release : 1993
Category : Mathematics
ISBN : 0821811797
This book presents an elementary and self-contained approach to Abelian varieties, a subject that plays a central role in algebraic and analytic geometry, number theory, and complex analysis. The book is based on notes from a course given at Concordia University and would be useful for independent study or as a textbook for graduate courses in complex analysis, Riemann surfaces, number theory, or analytic geometry. Murty works mostly over the complex numbers, discussing the theorem of Abel-Jacobi and Lefschetz's theorem on projective embeddings. After presenting some examples, Murty touches on Abelian varieties over number fields, as well as the conjecture of Tate (Faltings's theorem) and its relation to Mordell's conjecture. References are provided to guide the reader in further study.
Author : Gerard B. M. van der Geer
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 13,37 MB
Release : 2006-11-24
Category : Mathematics
ISBN : 0817644474
Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections