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comparison of cohomology

Journal of the Institute of Mathematics of Jussieu (1)

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COMPARISON OF KUMMER LOGARITHMIC TOPOLOGIES WITH CLASSICAL TOPOLOGIES
Part of
- (Co)homology theory
Heer Zhao
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 3 / May 2023

Published online by Cambridge University Press:

27 July 2021, pp. 1087-1117

Print publication:

May 2023
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We compare the Kummer flat (resp., Kummer étale) cohomology with the flat (resp., étale) cohomology with coefficients in smooth commutative group schemes, finite flat group schemes, and Kato’s logarithmic multiplicative group. We are particularly interested in the case of algebraic tori in the Kummer flat topology. We also make some computations for certain special cases of the base log scheme.