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DERIVED LOGARITHMIC GEOMETRY I

Part of: Commutative algebra: Homological methods Families, fibrations Algebraic geometry: Foundations

Published online by Cambridge University Press:  28 October 2014

Steffen Sagave ,
Timo Schürg  and
Gabriele Vezzosi
Steffen Sagave
Affiliation:
Department of Mathematics and Informatics, Bergische Universität Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany (sagave@math.uni-wuppertal.de)
Timo Schürg
Affiliation:
University of Augsburg, Universitätsstr. 14, 86159 Augsburg, Germany (timo.schuerg@math.uni-augsburg.de)
Gabriele Vezzosi
Affiliation:
Institut de Mathématiques de Jussieu - UMR7586 Batiment Sophie Germain, Case 7012, 75205 PARIS Cedex 13, France (gabriele.vezzosi@math.imj-prg.fr) DiMaI, Università di Firenze, Firenze, Italy
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Abstract

In order to develop the foundations of derived logarithmic geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log-étale maps, and use them to define derived log stacks.

Keywords

log structuresderived algebraic geometrycotangent complexsimplicial commutative rings

MSC classification

Primary: 14A20: Generalizations (algebraic spaces, stacks) 14D23: Stacks and moduli problems 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 2 , April 2016 , pp. 367 - 405
Copyright
© Cambridge University Press 2014 

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