SMS scnews item created by Stephan Tillmann at Tue 26 Jul 2016 1554
Type: Seminar
Modified: Tue 26 Jul 2016 1555
Distribution: World
Expiry: 25 Oct 2016
Calendar1: 3 Aug 2016 1200-1300
CalLoc1: Carslaw 535A
CalTitle1: Artinâ€™s conjecture for abelian varieties
Auth: tillmann@p710.pc (assumed)

Artin’s conjecture for abelian varieties

Cristian Virdol (Yonsei)

Wednesday 3 August 2016 from 12:00–13:00 in Carslaw 535A

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.