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Crystalline Chebotarev density theorems

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Speaker: 
Ambrus Pal
Affiliation: 
Imperial College London/MPI
Date: 
Wed, 17/12/2014 - 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

I formulate a conjectural analogue of Chebotarev's density theorem for convergent F-isocrystals over a smooth geometrically irreducible curve defined over a finite field using the Tannakian formalism. I will talk about the proof of this analogue in several special classes, including all semi-simple convergent F-isocrystals which have a filtration by isoclinic F-isocrystals of pair-wise different slopes whose monodromy groups are reductive and abelian over a non-empty open subcurve. The methods used include the theory of reductive groups and p-adic analysis, but at some point also a little bit of diophantine geometry, too. This is joint work with Urs Hartl.

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