Author:
Krishnamoorthy Raju,Pál Ambrus
Abstract
AbstractLet $$X/\mathbb {F}_{q}$$
X
/
F
q
be a smooth, geometrically connected variety. For X projective, we prove a Lefschetz-style theorem for abelian schemes of $$\text {GL}_2$$
GL
2
-type on X, modeled after a theorem of Simpson. Inspired by work of Corlette-Simpson over $$\mathbb {C}$$
C
, we formulate a conjecture that absolutely irreducible rank 2 local systems with infinite monodromy on X come from families of abelian varieties. We have the following application of our main result. If one assumes a strong form of Deligne’s (p-adic) companions conjecture from Weil II, then our conjecture for projective varieties reduces to the conjecture for projective curves. We also answer affirmitavely a question of Grothendieck on extending abelian schemes via their p-divisible groups.
Funder
Bergische Universität Wuppertal
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Mathematics
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献