Kolyvagin Systems
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Kolyvagin Systems
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Kolyvagin Systems written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Kolyvagin Systems
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Author : Barry Mazur
language : en
Publisher: Amer Mathematical Society
Release Date : 2004
Kolyvagin Systems written by Barry Mazur and has been published by Amer Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Since their introduction by Kolyvagin, Euler systems have been used in several important applications in arithmetic algebraic geometry. For a $p$-adic Galois module $T$, Kolyvagin's machinery is designed to provide an upper bound for the size of the Selmer group associated to the Cartier dual $T^*$. Given an Euler system, Kolyvagin produces a collection of cohomology classes which he calls ``derivative'' classes. It is these derivative classes which are used to bound the dual Selmer group. The starting point of the present memoir is the observation that Kolyvagin's systems of derivative classes satisfy stronger interrelations than have previously been recognized. We call a system of cohomology classes satisfying these stronger interrelations a Kolyvagin system. We show that the extra interrelations give Kolyvagin systems an interesting rigid structure which in many ways resembles (an enriched version of) the ``leading term'' of an $L$-function. By making use of the extra rigidity we also prove that Kolyvagin systems exist for many interesting representations for which no Euler system is known, and further that there are Kolyvagin systems for these representations which give rise to exact formulas for the size of the dual Selmer group, rather than just upper bounds.
Mod P L Functions And Analytic Kolyvagin Systems
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Author : Samuel Rufus Williams
language : en
Publisher:
Release Date : 2001
Mod P L Functions And Analytic Kolyvagin Systems written by Samuel Rufus Williams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Curves, Elliptic categories.
On Euler Systems Of Rank R And Their Kolyvagin Systems
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Author :
language : en
Publisher:
Release Date : 2009
On Euler Systems Of Rank R And Their Kolyvagin Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Kolyvagin Systems Over An Iwasawa Algebra
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Author : Kazim Buyukboduk
language : en
Publisher:
Release Date : 2007
Kolyvagin Systems Over An Iwasawa Algebra written by Kazim Buyukboduk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
In this thesis we study Kolyvagin Systems, as defined by Mazur and Rubin, over the cyclotomic Zp -tower for a Gal Q,Q representation T, which is free of finite rank over Zp . We prove, under certain hypotheses, that the module Kolyvagin Systems over Λ is free of rank one over the (cyclotomic) Iwasawa Algebra Λ. We also prove that, if T is exceptional in a certain sense, Kolyvagin Systems should specialize to zero under the map induced from the canonical map from T ⊗ Λ to T. In the spirit of Perrin-Riou's work on p-adic L-functions and Rubin's relevant conjectures in connection with Euler systems, we include a conjectural picture about how to relate the Kolyvagin systems to p-adic L-functions. We also study the Iwasawa theory of Stark units via the perspective offered by our main theorem, and provide a strategy to deduce the main conjectures of Iwasawa theory for totally real number fields.
On Howard S Main Conjecture And The Heegner Point Kolyvagin System
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Author : Murilo Corato Zanarella
language : en
Publisher:
Release Date : 2019
On Howard S Main Conjecture And The Heegner Point Kolyvagin System written by Murilo Corato Zanarella and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
We upgrade Howard's divisibility toward Perrin-Riou's Heegner point Main Conjecture to an equality under some mild conditions. As in the recent result of Burungale, Castella and Kim, we do this by exploiting Wei Zhang's proof of the Kolyvagin conjecture but, unlike their result, we do not restrict ourselves to the case of analytic rank 1 over K. The main ingredient for this is an improvement of Howard's Kolyvagin system formalism. As another consequence of this improvement, we establish the equivalence between this main conjecture and the primitivity of the Kolyvagin system in certain cases, by also exploiting a explicit reciprocity law for Heegner points.
Euler Systems Am 147 Volume 147
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Author : Karl Rubin
language : en
Publisher: Princeton University Press
Release Date : 2014-09-08
Euler Systems Am 147 Volume 147 written by Karl Rubin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-08 with Mathematics categories.
One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.
The Heegner Point Kolyvagin System
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Author : Benjamin Howard
language : en
Publisher:
Release Date : 2002
The Heegner Point Kolyvagin System written by Benjamin Howard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Stark S Conjectures Recent Work And New Directions
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Author : David Burns
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Stark S Conjectures Recent Work And New Directions written by David Burns and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Education categories.
Stark's conjectures on the behavior of USDLUSD-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory. The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to themes currently under exploration in the area, such as non-abelian and USDpUSD-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and interested in number theory.
Kolyvagin S Method For Shimura Varieties
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Author : D. Yu Logachev
language : en
Publisher:
Release Date : 1996
Kolyvagin S Method For Shimura Varieties written by D. Yu Logachev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.