Independence of for Frobenius conjugacy classes attached to abelian varieties

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Rong Zhou, Imperial College London

Please note the time change for this seminar

Zoom link:

https://theias.zoom.us/j/959183254(link is external)

Password: the three digit integer that is the cube of the sum of its digits

 

Let A be an abelian variety over a number field EC and let v be a place of good reduction lying over a prime p. For a prime p, a result of Deligne implies that upon replacing E by a finite extension, the Galois representation on the -adic Tate module of A factors as ρ:Gal(¯E/E)GA, where GA is the Mumford--Tate group of AC. For p>2, we prove that the conjugacy class of  ρ(Frobv) is defined over Q and independent of . This is joint work with Mark Kisin.