`Artin's conjecture for abelian varieties'

by Dr. Cristian Virdol (Yonsei University, Republic of Korea)

Tuesday, February 20, 2018 from 11:30 to 12:30 (Asia/Kolkata)
at TIFR, Mumbai ( AG-77 )

Description

Abstract
Artin's primitive root conjecture (1927) states that, for any
integer $a\neq\pm1$  or a perfect square, there are infinitely many primes
$p$  for which a  is a primitive root (mod $p$). This conjecture is not
known for any specific $a$. In my talk I will prove the equivalent of this
conjecture unconditionally for general abelian varieties for all $a$.
Moreover, under GRH, I will prove the strong form of Artin's conjecture
(1927) for abelian varieties, i.e., I will prove the density and the
asymptotic formula for the primitive primes.