Algebra & Number Theory

Moduli of morphisms of logarithmic schemes

Jonathan Wise

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We show that there is a logarithmic algebraic space parameterizing logarithmic morphisms between fixed logarithmic schemes when those logarithmic schemes satisfy natural hypotheses. As a corollary, we obtain the representability of the stack of stable logarithmic maps from logarithmic curves to a fixed target without restriction on the logarithmic structure of the target.

An intermediate step requires a left adjoint to pullback of étale sheaves, whose construction appears to be new in the generality considered here, and which may be of independent interest.

Article information

Algebra Number Theory, Volume 10, Number 4 (2016), 695-735.

Received: 14 September 2014
Revised: 28 October 2015
Accepted: 22 March 2016
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14D23: Stacks and moduli problems 14A20: Generalizations (algebraic spaces, stacks)

logarithmic geometry moduli


Wise, Jonathan. Moduli of morphisms of logarithmic schemes. Algebra Number Theory 10 (2016), no. 4, 695--735. doi:10.2140/ant.2016.10.695.

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