**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)

### Geometry & Topology

# Artin’s conjecture for abelian varieties

### Cristian Virdol (Yonsei)

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

Please join us for lunch after the talk!

**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.