Skip to main content
NCBI home page
Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1972 Sep;69(9):2614–2616. doi: 10.1073/pnas.69.9.2614

Cohomology of Various Completions of Quasicoherent Sheaves on Affines

Olav Arnfinn Laudal 1,2
PMCID: PMC427000  PMID: 16592014

Abstract

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 M̃ 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, Hi(X,M̃+) = O for i ≥ 1, H°(X,M̃+) = M+.

Full text

PDF
2614

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Monsky P., Washnitzer G. THE CONSTRUCTION OF FORMAL COHOMOLOGY SHEAVES. Proc Natl Acad Sci U S A. 1964 Dec;52(6):1511–1514. doi: 10.1073/pnas.52.6.1511. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Proceedings of the National Academy of Sciences of the United States of America are provided here courtesy of National Academy of Sciences

RESOURCES