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Local indices of \(p\)-adic differential operators corresponding to Artin-Schreier-Witt coverings. (English) Zbl 0849.12013

From the author’s introduction: In this paper we study local indices of \(p\)-adic differential operators derived from \(p\)-adic representations [as defined by P. Robba, Ann. Inst. Fourier 35, 13-55 (1985; Zbl 0566.12017)]. The main result of this paper is that, for a complete discrete valuation ring of characteristic \(p > 2\) with perfect residue field, the Swan conductor of a representation of rank 1 is equal to the local index of the corresponding \(p\)-adic differential operator, as conjectured by R. Crew [cf. Algebraic geometry, Proc. Symp. Pure Math. 46, 111-138 (1987; Zbl 0639.14011)].

MSC:

12H25 \(p\)-adic differential equations
14F30 \(p\)-adic cohomology, crystalline cohomology
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