Seminars
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
Calendar
Search
Add a seminar

RSS
Forthcoming seminars




Shafarevich Seminar
January 25, 2022 15:00, Moscow, Steklov Mathematical Institute, Room. 104 (8 Gubkina) + Zoom
 


Reduction of abelian varieties and a conjecture of Agashe

M. Melistas

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Video records:
MP4 3,565.2 Mb
MP4 2,207.3 Mb

Number of views:
This page:305
Video files:69



Abstract: This talk will consist of two parts. First, reduction properties of abelian varieties defined over a field K that have a K-rational point of order p will be studied. Here K is a field of characteristic 0 equipped with a discrete valuation which has algebraically closed residue field of characteristic p. After presenting a general result, we will focus on the dimension 1 case and classify the possible Kodaira types of reduction that can occur. In the second part of the talk, we will discuss a conjecture of Agashe, which is a consequence of the Birch and Swinnerton-Dyer (BSD) conjecture for elliptic curves over the rationals. We will present a theorem that proves Agashe's conjecture. The connection between the two parts is that we can put restrictions on torsion subgroups of certain twists of elliptic curves using reduction.

Language: English
 
  Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024