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Author Mazur, Barry ♦ Pacetti, Ariel ♦ Voight, John
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Elliptic Curve ♦ Euler System ♦ Introductory Lecture Euler System ♦ Selmer Group ♦ P-adic Main Conjecture ♦ Class Group ♦ Student Presentation ♦ Hour Lecture ♦ Compatible Cohomology Class ♦ Birch-swinnerton-dyer Conjecture ♦ Cyclotomic Tower ♦ Mordell-weil Group ♦ Heegner Point Euler System ♦ Ideal Class Group ♦ Anti-cyclotomic Tower ♦ Kolyvagin System ♦ Main Conjecture ♦ Safarevich-tate Group
Abstract The purpose of these notes is to describe the notion of an Euler system, a collection of compatible cohomology classes arising from a tower of fields that can be used to bound the size of Selmer groups. There are applications to the study of the ideal class group, Iwasawa’s main conjecture, Mordell-Weil group of an elliptic curve, X (the Safarevich-Tate group), Birch-Swinnerton-Dyer conjecture, and a study of the p-adic main conjecture for elliptic curves. For a reference, consult [R 1], the bibliography there, and also [R 2]. Our group will be giving four hour lectures, as the schedule indicates, as follows: 1. Introduction to Euler Systems and Kolyvagin Systems. (B.M.) 2. L-functions and applications of Euler systems to ideal class groups (ascending cyclotomic towers over Q). (T.W.) 3. Student presentation: The “Heegner point ” Euler System and applications to the Selmer groups of elliptic curves (ascending anti-cyclotomic towers over quadratic
Description This content is published in/by Harvard University
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study