CRYSTALLINE REPRESENTATIONS OF GQpa WITH COEFFICIENTS
نویسنده
چکیده
We systematically classify strongly divisible φ-lattices, and present an explicit way to construct embedded Wach modules that correspond to crystalline representations with coefficients of the local absolute Galois group GQpa , where Qpa is the unramified extension of Qp of degree a. As applications we prove a theorem of Fontaine-Laffaille type on existence of integral Wach module when σ-invariant Hodge-Tate weight < p − 1 and we also show p-adic continuity of embedded Wach modules. We classify irreducible crystalline representations of GQpa which generalizes a result of Breuil. Finally we construct some analytic family of 2-dimensional representations of GQpa with coefficients, and establish some result of reduction types modulo p for these representations.
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