Vol. 10, No. 4, 2016

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Moduli of morphisms of logarithmic schemes

Jonathan Wise

Vol. 10 (2016), No. 4, 695–735
DOI: 10.2140/ant.2016.10.695
Abstract

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.

Keywords
logarithmic geometry, moduli
Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 14D23, 14A20
Milestones
Received: 14 September 2014
Revised: 28 October 2015
Accepted: 22 March 2016
Published: 20 June 2016
Authors
Jonathan Wise
Department of Mathematics
University of Colorado
Campus Box 395
Boulder, CO 80309-0395
United States