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CMI-IMSc Number Theory Seminar
Date: Tuesday, 26 March 2024
Time: 12:00 – 1:00 PM
Venue: Lecture Hall 803, CMI
Nonexistence and Finiteness Theorems for Certain Abelian Varieties
Plawan Das
Chennai Mathematical Institute.
26-03-24

Abstract

This talk will discuss some non-existence and finiteness theorems for Galois representations and their applications in arithmetic geometry. In particular, we will talk about the Shafarevich Conjecture (proved by Faltings in 1983) for abelian varieties defined over number fields; and the Rasmussen-Tamagawa Conjecture (2008) which is a finiteness conjecture on abelian varieties defined over number fields with constrained prime power torsion and is still wide open.

Also, I will present some recent works with Prof. C. S. Rajan on generalizations of the Shafarevich conjecture and its application to prove some special cases of the Rasmussen-Tamagawa Conjecture which is a joint work with Dr. Subham Sarkar.