The Weil-etale topology for number rings

• 成果类型: Article
• 署名作者: Lichtenbaum, Stephen
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.170.657
• 发表日期: 2009
• 页码: 657-683
• 关键词: cohomology

摘要

There should be a Grothendieck topology for an arithmetic scheme X such that the Euler characteristic of the cohomology groups of the constant sheaf Z with compact support at infinity gives, up to sign, the leading term of the zeta-function of X at s = 0. We construct a topology (the Weil-etale topology) for the ring of integers in a number field whose cohomology groups H-i (Z) determine such an Euler characterstic if we restrict to i <= 3.