Laudal O A
Department of Mathematics, University of Oslo, Blindein, Oslo, Norway.
Proc Natl Acad Sci U S A. 1972 Sep;69(9):2614-6. doi: 10.1073/pnas.69.9.2614.
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(+).
设(O)为完备离散赋值环，(A)为交换(O)-代数。设(M)为任意(A)-模。本文研究了一类与(A)相对应的仿射簇(X)上的完备化(M)，其中包括例如瓦施尼策 - 蒙斯基完备化[1]以及全完备化。然后我们证明，对于所有这些完备化，当(i\geq1)时，(H^i(X,M^+) = O)，(H^0(X,M^+) = M^+)。
