Algebra & Number Theory
- Algebra Number Theory
- Volume 10, Number 4 (2016), 695-735.
Moduli of morphisms of logarithmic schemes
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.
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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Wise, Jonathan. Moduli of morphisms of logarithmic schemes. Algebra Number Theory 10 (2016), no. 4, 695--735. doi:10.2140/ant.2016.10.695. https://projecteuclid.org/euclid.ant/1510842512