Rank 2 local systems and abelian varieties

Publication available at: https://arxiv.org/abs/1809.02106
Title: Rank 2 local systems and abelian varieties
Authors: Krishnamoorthy, R
Pal, A
Item Type: Working Paper
Abstract: LetX/Fqbe a smooth geometrically connected variety. Inspired by work of Corlette-Simpson overC, we formulate a conjecture that absolutely irreducible rank 2 local systems withinfinite monodromy onX“come from families of abelian varieties”. WhenXis a projective variety,we prove that ap-adic variant of this conjecture reduces to the case of projective curves. If oneassumes a strong form of Deligne’s (p-adic)companions conjecturefrom Weil II, this implies that thel-adic version of our conjecture for projective varieties also reduces to the case of projective curves.Along the way we prove Lefschetz theorems for homomorphismsof abelian schemes and Barsotti-Tategroups. We also answer affirmitavely a question of Grothendieck on extending abelian schemes viatheirp-divisible groups.
Issue Date: 11-Oct-2018
URI: http://hdl.handle.net/10044/1/66467
Copyright Statement: © 2018 The Author(s)
Open Access location: https://arxiv.org/abs/1809.02106
Appears in Collections:Pure Mathematics

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