A sheaf of Hochschild complexes on quasi-compact opens

Details A sheaf of Hochschild complexes on quasi-compact opens A sheaf of Hochschild complexes on quasi-compact opens

2007-07-17

arxiv.org/abs/0707.2605v1

Mathematics

Algebraic Geometry

7 pages. To appear in Proc. Amer. Math. Soc

Scientific paper

For a scheme X, we construct a sheaf C of complexes on X such that for every
quasi-compact open subset U of X, C(U) is quasi-isomorphic to the Hochschild
complex of the scheme U. Since C is moreover acyclic for taking sections on
quasi-compact opens, we obtain a local to global spectral sequence for
Hochschild cohomology if X is quasi-compact.

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