Espaces de Banach analytiques p-adiques et espaces de Banach-Colmez

Abstract : A p-adic spectral Banach space is a p-adic Banach space endowed with an algebra of analytic functions with values in a complete, algebraically closed field C. A Banach-Colmez space is such a p-adic spectral Banach space that can be built via successive extensions and quotients from C and Qp. These spaces make an abelian category, and two additive functions, « dimension » and « height », are naturally defined ; this gives a new proof of the « weakly admissible implies admissible » theorem (Colmez-Fontaine, 2000). Moreover, there exists a full subcategory whose objects are canonically filtered by the slopes of the Frobenius action ; this filtration is decreasing and indexed by the non-negative rational numbers.
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Submitted on : Tuesday, January 19, 2010 - 3:29:31 PM
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Jérôme Plût. Espaces de Banach analytiques p-adiques et espaces de Banach-Colmez. Mathématiques [math]. Université Paris Sud - Paris XI, 2009. Français. ⟨tel-00448628⟩

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