Cohomology and base change for algebraic stacks

Jack Hall

doi:10.1007/s00209-014-1321-7

Cohomology and base change for algebraic stacks

Jack Hall

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We prove that cohomology and base change holds for algebraic stacks, generalizing work of Brochard in the tame case. We also show that Hom-spaces on algebraic stacks are represented by abelian cones, generalizing results of Grothendieck, Brochard, Olsson, Lieblich, and Roth–Starr. To accomplish all of this, we prove that a wide class of relative Ext-functors in algebraic geometry are coherent (in the sense of M. Auslander).

Original language	English (US)
Pages (from-to)	401-429
Number of pages	29
Journal	Mathematische Zeitschrift
Volume	278
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-014-1321-7
State	Published - Sep 11 2014
Externally published	Yes

Keywords

Algebraic stacks
Cohomology
Derived categories
Hom space

ASJC Scopus subject areas

General Mathematics

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10.1007/s00209-014-1321-7

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AB - We prove that cohomology and base change holds for algebraic stacks, generalizing work of Brochard in the tame case. We also show that Hom-spaces on algebraic stacks are represented by abelian cones, generalizing results of Grothendieck, Brochard, Olsson, Lieblich, and Roth–Starr. To accomplish all of this, we prove that a wide class of relative Ext-functors in algebraic geometry are coherent (in the sense of M. Auslander).

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KW - Cohomology

KW - Derived categories

KW - Hom space

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Cohomology and base change for algebraic stacks

Abstract

Keywords

ASJC Scopus subject areas

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