Independence of ℓ for Frobenius conjugacy classes attached to abelian varieties
Independence of ℓ 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 E⊂C and let v be a place of good reduction lying over a prime p. For a prime ℓ≠p, a result of Deligne implies that upon replacing E by a finite extension, the Galois representation on the ℓ-adic Tate module of A factors as ρℓ:Gal(¯E/E)→GA, where GA is the Mumford--Tate group of AC. For p>2, we prove that the conjugacy class of ρℓ(Frobv) is defined over Q and independent of ℓ. This is joint work with Mark Kisin.