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2010 On ramification filtrations and $p$-adic differential modules, I: the equal characteristic case
Liang Xiao
Algebra Number Theory 4(8): 969-1027 (2010). DOI: 10.2140/ant.2010.4.969

Abstract

Let k be a complete discretely valued field of equal characteristic p>0 with possibly imperfect residue field, and let Gk be its Galois group. We prove that the conductors computed by the arithmetic ramification filtrations on Gk defined by Abbes and Saito (Amer. J. Math 124:5, 879–920) coincide with the differential Artin conductors and Swan conductors of Galois representations of Gk defined by Kedlaya (Algebra Number Theory 1:3, 269–300). As a consequence, we obtain a Hasse–Arf theorem for arithmetic ramification filtrations in this case. As applications, we obtain a Hasse–Arf theorem for finite flat group schemes; we also give a comparison theorem between the differential Artin conductors and Borger’s conductors (Math. Ann. 329:1, 1–30).

Citation

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Liang Xiao. "On ramification filtrations and $p$-adic differential modules, I: the equal characteristic case." Algebra Number Theory 4 (8) 969 - 1027, 2010. https://doi.org/10.2140/ant.2010.4.969

Information

Received: 14 May 2009; Revised: 25 May 2010; Accepted: 22 June 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1225.11152
MathSciNet: MR2832631
Digital Object Identifier: 10.2140/ant.2010.4.969

Subjects:
Primary: 11S15
Secondary: 12H25 , 14G22

Keywords: $p$-adic differential equation , Artin conductors , Hasse–Arf theorem , ramification , Swan conductors

Rights: Copyright © 2010 Mathematical Sciences Publishers

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