Slope filtrations for relative Frobenius

By Kiran S. Kedlaya. 2006

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The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over the Robba ring (the ring of germs of rigid analytic functions on an unspecified open annulus of outer radius 1) over a discretely valued field. In this paper, we give a third-generation proof of this theorem, which both introduces some new simplifications (particularly the use of faithfully flat descent, to recover the theorem from a classification theorem of Dieudonne-Manin type) and extends the result to allow an arbitrary action on coefficients (previously the action on coefficients had to itself be a lift of an absolute Frobenius). This extension is relevant to a study of (phi, Gamma)-modules associated to families of p-adic Galois representations, presently being initiated by Berger and Colmez.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9d5e9e319c31ab7bd817a07437b2c20d242f6af5

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Citations in the corpus

Relative P-adic Hodge Theory: Foundations (2013, methodology): “Our description here is rather minimal; see [69] for a more detailed discussion.”