The adic tame site

  • Katharina Hübner

    Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmund J. Safra Campus, Israel
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Abstract

For every adic space we construct a site , the tame site of . For a scheme over a base scheme we obtain a tame site by associating with an adic space and considering the tame site . We examine the connection of the cohomology of the tame site with étale cohomology and compare its fundamental group with the conventional tame fundamental group. Finally, assuming resolution of singularities, for a regular scheme over a base scheme of characteristic we prove a cohomological purity theorem for the constant sheaf on . As a corollary we obtain homotopy invariance for the tame cohomology groups of .

Cite this article

Katharina Hübner, The adic tame site. Doc. Math. 26 (2021), pp. 873–945

DOI 10.4171/DM/832