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SUMMARY:Rong Zhou (Imperial)
DTSTART:20200520T150000Z
DTEND:20200520T160000Z
DTSTAMP:20260418T063712Z
UID:LNTS/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/5/">Ind
 ependence of $l$ for Frobenius conjugacy classes attached to abelian varie
 ties</a>\nby Rong Zhou (Imperial) as part of London number theory seminar\
 n\n\nAbstract\nLet $A$ be an abelian variety over a number field $E\\subse
 t \\mathbb{C}$ and let $v$ be a place of good reduction lying over a prime
  $p$. For a prime $l\\neq p$\, a theorem of Deligne implies that upon maki
 ng a finite extension of $E$\, the Galois representation on the $l$-adic T
 ate module factors as $\\rho_l:\\Gamma_E\\rightarrow G_A(\\mathbb{Q}_l)$\,
  where $G_A$ is the Mumford-Tate group of $A$. We prove that the conjugacy
  class of $\\rho_l(Frob_v)$  is defined over $\\mathbb{Q}$ and independent
  of $l$. This is joint work with Mark Kisin.\n
LOCATION:https://researchseminars.org/talk/LNTS/5/
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