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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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Seminars and Colloquia

Mathematics

Artin’s conjecture for abelian varieties 
 
Fri, Feb 23, 2018,   04:30 PM to 05:30 PM at Madhava Hall

Dr. Cristian Virdol
Yonsei University

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.
 
Thanks, 

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