School of Mathematics Seminars and Lectures
`Artin's conjecture for abelian varieties'
by Dr. Cristian Virdol (Yonsei University, Republic of Korea)
Tuesday, February 20, 2018
from
to
(Asia/Kolkata)
at TIFR, Mumbai ( AG-77 )
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. |