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2017 Logarithmic good reduction, monodromy and the rational volume
Arne Smeets
Algebra Number Theory 11(1): 213-233 (2017). DOI: 10.2140/ant.2017.11.213

Abstract

Let R be a strictly local ring complete for a discrete valuation, with fraction field K and residue field of characteristic p>0. Let X be a smooth, proper variety over K. Nicaise conjectured that the rational volume of X is equal to the trace of the tame monodromy operator on -adic cohomology if X is cohomologically tame. He proved this equality if X is a curve. We study his conjecture from the point of view of logarithmic geometry, and prove it for a class of varieties in any dimension: those having logarithmic good reduction.

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Arne Smeets. "Logarithmic good reduction, monodromy and the rational volume." Algebra Number Theory 11 (1) 213 - 233, 2017. https://doi.org/10.2140/ant.2017.11.213

Information

Received: 17 March 2016; Revised: 6 July 2016; Accepted: 10 August 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1361.14017
MathSciNet: MR3602769
Digital Object Identifier: 10.2140/ant.2017.11.213

Subjects:
Primary: 14F20
Secondary: 11G25, 11S15

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 1 • 2017
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