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p-adic semistable representations and generalization of the Shafarevich conjecture

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Breuil’s theory of semistable p-adic representations is applied to prove the following property: if X is a projective variety over Q with semistable reduction modulo 3 and good reduction at all p <> 3 then its Hodge number h^{2,0} = 0.

This talk is part of the Number Theory Seminar series.

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