Mathematical Research Letters

Volume 7 (2000)

Number 5

Crystalline subrepresentations and Neron models

Pages: 605 – 614

DOI: http://dx.doi.org/10.4310/MRL.2000.v7.n5.a6

Authors

Minhyong Kim

Susan H. Marshall

Abstract

We propose the notion of the {\em crystalline sub-representation functor} defined on $p$-adic representations of the Galois groups of finite extensions of ${\mathbb{Q}_p}$, with certain restrictions in the case of integral representations. By studying its right-derived functors, we find a natural extension of a formula of Grothendieck expressing the group of connected components of a Neron model of an abelian variety in terms of Galois cohomology.

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