On a theorem of Grothendieck
The authors prove the following analog of the result of A. Grothendieck on the cohomology of a coherent sheaf. Theorem. Let \(U\) be a local regular scheme of geometric type over a field \(k\) and \(T\to U\) be a smooth proper morphism. Let \(F\) be a locally constant constructible torsion étale sheaf on \(T\) with torsion prime to characteristic of \(k\). Then there exists a finite complex \(L\) of locally constant constructible sheaves on \(U\) and a functor isomorphism between étale hypercohomology \(H_{\text{ét}}^q(T\times_U U',F) \cong H_{\text{ét}}^q(U',L\times_U U')\), where \(q\geq 0\) and \(U'\) denotes an \(U\)-scheme.
scientific article; zbMATH DE number 2174358
scientific article