The Weil-étale topology for number rings

By S. Lichtenbaum. 2005

65 citations recorded by the source corpus.

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 Hl (Z) determine such an Euler characterstic if we restrict to / < 3.

Subfields: Geometry and Topology, Mathematical Physics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/9449018bd08e3db5c7b4a5be9960bece3f07bdd7