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In this paper we develop a theory of Grothendieck's six operations of lisse-étale constructible sheaves on Artin stacks locally of finite type over certain excellent schemes of finite Krull dimension. We also give generalizations of the classical base change theorems and Kunneth formula to stacks, and prove new results about cohomological descent for unbounded complexes.
@article{PMIHES_2008__107__109_0,
author = {Laszlo, Yves and Olsson, Martin},
title = {The six operations for sheaves on {Artin} stacks {I:} {Finite} coefficients},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {109--168},
publisher = {Institut des Hautes \'Etudes Scientifiques},
volume = {107},
year = {2008},
doi = {10.1007/s10240-008-0011-6},
mrnumber = {2434692},
zbl = {1191.14002},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-008-0011-6/}
}
TY - JOUR AU - Laszlo, Yves AU - Olsson, Martin TI - The six operations for sheaves on Artin stacks I: Finite coefficients JO - Publications Mathématiques de l'IHÉS PY - 2008 SP - 109 EP - 168 VL - 107 PB - Institut des Hautes Études Scientifiques UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-008-0011-6/ DO - 10.1007/s10240-008-0011-6 LA - en ID - PMIHES_2008__107__109_0 ER -
%0 Journal Article %A Laszlo, Yves %A Olsson, Martin %T The six operations for sheaves on Artin stacks I: Finite coefficients %J Publications Mathématiques de l'IHÉS %D 2008 %P 109-168 %V 107 %I Institut des Hautes Études Scientifiques %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-008-0011-6/ %R 10.1007/s10240-008-0011-6 %G en %F PMIHES_2008__107__109_0
Laszlo, Yves; Olsson, Martin. The six operations for sheaves on Artin stacks I: Finite coefficients. Publications Mathématiques de l'IHÉS, Tome 107 (2008), pp. 109-168. doi: 10.1007/s10240-008-0011-6
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