Cohomology and base change for algebraic stacks

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9 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 languageEnglish (US)
Pages (from-to)401-429
Number of pages29
JournalMathematische Zeitschrift
Volume278
Issue number1-2
DOIs
Publication statusPublished - Sep 11 2014
Externally publishedYes

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Keywords

  • Algebraic stacks
  • Cohomology
  • Derived categories
  • Hom space

ASJC Scopus subject areas

  • Mathematics(all)

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