`Artin's conjecture for abelian varieties'

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

Tuesday 20 Feb 2018, 11:30 → 12:30 Asia/Kolkata

AG-77 (TIFR, Mumbai)

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.