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Rank 2 local systems and abelian varieties

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Speaker: 
Raju Krishnamoorthy
Affiliation: 
University of Georgia
Date: 
Tue, 2020-02-18 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk
Let X/k be a smooth variety over a finite field. Motivated by
work of Corlette-Simpson over the complex numbers, we formulate a
conjecture that certain rank 2 local systems on X come from families of
abelian varieties. After an introduction to l/p-adic companions, we explain
how the existence of p-adic companions can be used to approach the
conjecture via a Lefschetz-style theorem for families of abelian varieties
in positive characteristic. This is joint work with A. Pál.
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