Cohomology and base change for algebraic stacks

Research output: Contribution to journalArticle

9 Scopus citations


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
Issue number1-2
StatePublished - Sep 11 2014
Externally publishedYes


  • Algebraic stacks
  • Cohomology
  • Derived categories
  • Hom space

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Cohomology and base change for algebraic stacks'. Together they form a unique fingerprint.

  • Cite this