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Slope filtrations revisited. (English) Zbl 1081.14028
Doc. Math. 10, 447-525 (2005); erratum 12, 361-362 (2007).
From the text: We give a “second generation” exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of U. Hartl and R. Pink [Compos. Math. 140, No. 3, 689–716 (2004; Zbl 1074.14028)], which points out some analogies with the formalism of stable vector bundles.
From the erratum: “Laurent Berger has pointed out that the construction of Teichmüller presentations in Definition 2.5.1 of the paper cited in the heading is not valid: it fails to properly account for the nonlinearity of the Teichmüller map. This would appear to invalidate the results of that paper, depending on the use of Teichmüller presentations, or on plus-minus-zero presentations. Fortunately, these can be corrected by adapting the technique of strong semiunit decompositions from [the author, Ann. Math. (2) 160, No. 1, 93–184 (2004; Zbl 1088.14005)].

14F30 \(p\)-adic cohomology, crystalline cohomology
11G25 Varieties over finite and local fields
12H25 \(p\)-adic differential equations
14G22 Rigid analytic geometry
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