TY - JOUR
T1 - Cohomology and base change for algebraic stacks
AU - Hall, Jack
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2014/9/11
Y1 - 2014/9/11
N2 - 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).
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 - http://www.scopus.com/inward/record.url?scp=84939891250&partnerID=8YFLogxK
U2 - 10.1007/s00209-014-1321-7
DO - 10.1007/s00209-014-1321-7
M3 - Article
SN - 0025-5874
VL - 278
SP - 401
EP - 429
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1-2
ER -