Definition of Shimura curves in positive characteristics
-- Jie Xia, March 14, 2014

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Classical Shimura varieties are defined over
the complex field and generally have number fields as the field of
definition. Motivated by an example constructed by Mumford, we
find conditions which guarantee that a curve in char. p lifts to a
Shimura curve of Hodge type. The conditions are intrinsic in
positive characteristics. So we can take them as the definition
of Shimura curves in char. p. 
                              

In this talk, I will first discuss Mumford's example, and
then present such conditions in terms of Dieudonne crystals,
crystalline Hodge cycles and l-adic monodromy. One of the key
ingredients in the proofs is a deformation result on versally
deformed Barsotti-Tate groups.