Cohomology of various completions of quasicoherent sheaves on affines.
Let O be a complete discrete valuation ring and let A be a commutative O-algebra. Let M be any A-module. In this paper, a class of completions M on the affine X corresponding to A, which includes, e.g., the Washnitzer-Monsky completion [1], and the full completion is studied. We then prove that for all of these completions we have, H(i)(X,M(+)) = O for i >/= 1, H degrees (X,M(+)) = M(+).
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Department of Mathematics, University of Oslo, Blindein, Oslo, Norway.