Logarithmic De Rham, Infinitesimal and Betti Cohomologies

Details Logarithmic De Rham, Infinitesimal and Betti Cohomologies Logarithmic De Rham, Infinitesimal and Betti Cohomologies

2004-07-23

arxiv.org/abs/math/0407402v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

In this article, we analyze the connection between the Log De Rham Cohomology of an fs (not necessary log smooth) log scheme $Y$ over $\mathbb C$ (for $Y$ admitting an exact closed immersion into an fs log smooth log scheme over $\mathbb C$), its Log Infinitesimal Cohomology $H^{^.}(Y^{log}_{inf}, \mathcal O_{Y^{log}_{inf}})$, and its Log Betti Cohomology, which is the Cohomology of its associated Kato-Nakayama topological space $Y^{an}_{log}$, and we prove that they are isomorphic. These results are the log scheme analogues of two classical comparison theorems.

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