On Howard S Main Conjecture And The Heegner Point Kolyvagin System
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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.
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.
Nine Mathematical Challenges An Elucidation
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Author : A. Kechris
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-24
Nine Mathematical Challenges An Elucidation written by A. Kechris 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 2021-09-24 with Education categories.
This volume stems from the Linde Hall Inaugural Math Symposium, held from February 22–24, 2019, at California Institute of Technology, Pasadena, California. The content isolates and discusses nine mathematical problems, or sets of problems, in a deep way, but starting from scratch. Included among them are the well-known problems of the classification of finite groups, the Navier-Stokes equations, the Birch and Swinnerton-Dyer conjecture, and the continuum hypothesis. The other five problems, also of substantial importance, concern the Lieb–Thirring inequalities, the equidistribution problems in number theory, surface bundles, ramification in covers and curves, and the gap and type problems in Fourier analysis. The problems are explained succinctly, with a discussion of what is known and an elucidation of the outstanding issues. An attempt is made to appeal to a wide audience, both in terms of the field of expertise and the level of the reader.
Heegner Points And Rankin L Series
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Author : Henri Darmon
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-21
Heegner Points And Rankin L Series written by Henri Darmon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-21 with Mathematics categories.
Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments.
Kolyvagin Systems
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Author : Barry Mazur
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Kolyvagin Systems written by Barry Mazur 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 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.
Elliptic Curves Modular Forms And Iwasawa Theory
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Author : David Loeffler
language : en
Publisher: Springer
Release Date : 2017-01-15
Elliptic Curves Modular Forms And Iwasawa Theory written by David Loeffler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-15 with Mathematics categories.
Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.
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.
Heegner Modules And Elliptic Curves
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2004
Heegner Modules And Elliptic Curves written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Algebraic fields categories.
A Collection Of Manuscripts Written In Honour Of Kazuya Kato On The Occasion Of His Fiftieth Birthday
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Author : Spencer Bloch
language : en
Publisher:
Release Date : 2003
A Collection Of Manuscripts Written In Honour Of Kazuya Kato On The Occasion Of His Fiftieth Birthday written by Spencer Bloch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Algebraic fields categories.
P Adic Monodromy And The Birch And Swinnerton Dyer Conjecture
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Author : Glenn Stevens
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
P Adic Monodromy And The Birch And Swinnerton Dyer Conjecture written by Glenn Stevens 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 1994 with Mathematics categories.
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.