Algebra & Number Theory
- Algebra Number Theory
- Volume 11, Number 1 (2017), 213-233.
Logarithmic good reduction, monodromy and the rational volume
Let be a strictly local ring complete for a discrete valuation, with fraction field and residue field of characteristic . Let be a smooth, proper variety over . Nicaise conjectured that the rational volume of is equal to the trace of the tame monodromy operator on -adic cohomology if is cohomologically tame. He proved this equality if 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.
Algebra Number Theory, Volume 11, Number 1 (2017), 213-233.
Received: 17 March 2016
Revised: 6 July 2016
Accepted: 10 August 2016
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14F20: Étale and other Grothendieck topologies and (co)homologies
Secondary: 11G25: Varieties over finite and local fields [See also 14G15, 14G20] 11S15: Ramification and extension theory
Smeets, Arne. Logarithmic good reduction, monodromy and the rational volume. Algebra Number Theory 11 (2017), no. 1, 213--233. doi:10.2140/ant.2017.11.213. https://projecteuclid.org/euclid.ant/1510842718