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^*

^*Corresponding author for this work

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

18 Citations (Scopus)

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
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
Publication status	Published - 11 Sept 2014

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title = "Cohomology and base change for algebraic stacks",

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).",

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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).

KW - Algebraic stacks

KW - Cohomology

KW - Derived categories

KW - Hom space

UR - https://www.scopus.com/pages/publications/84939891250

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

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ER -

Cohomology and base change for algebraic stacks

Abstract

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