منابع مشابه
Sheaves on Artin Stacks
We develop a theory of quasi–coherent and constructible sheaves on algebraic stacks correcting a mistake in the recent book of Laumon and Moret-Bailly. We study basic cohomological properties of such sheaves, and prove stack–theoretic versions of Grothendieck’s Fundamental Theorem for proper morphisms, Grothendieck’s Existence Theorem, Zariski’s Connectedness Theorem, as well as finiteness Theo...
متن کاملFormal Gaga on Artin Stacks
Suppose X is a locally noetherian Deligne–Mumford stack. Definition 1.2 has an obvious variant X̂ét using the underlying smaller étale site Xét and the restriction Oc Xét of Oc X to this site. By [3, 12.7.4], the category of cartesian Oc X -modules on Xlis-ét is equivalent to the category of Oc Xét-modules on Xét: (1.1) ModXlis-ét,cart(Oc X ) ' ModXét(Oc Xét) Definition 1.3. Let X be a locally n...
متن کاملOn proper coverings of Artin stacks
We prove that every separated Artin stack of finite type over a noetherian base scheme admits a proper covering by a quasi–projective scheme. An application of this result is a version of the Grothendieck existence theorem for Artin stacks.
متن کاملCycle groups for Artin stacks
We construct an algebraic homology functor for Artin stacks of finite type over a field, and we develop intersection-theoretic properties. DOI: 10.1007/s002220050351 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: http://doi.org/10.5167/uzh-22143 Accepted Version Originally published at: Kresch, A (1999). Cycle groups for Artin stacks. Inventiones Mathematicae, ...
متن کاملTangent Lie algebra of derived Artin stacks
Since the work of Mikhail Kapranov in [Kap], it is known that the shifted tangent complex TX r ́1s of a smooth algebraic variety X is endowed with a weak Lie structure. Moreover any complex of quasi-coherent sheaves on X is endowed with a weak Lie action of this tangent Lie algebra. We will generalize this result to (finite enough) derived Artin stacks, without any smoothness assumption. This in...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2018
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-018-2129-7