1207.0276Jul 2, 2012Besides having cleaner exposition, this version adds a counterexample for etale cohomology. Some sheaves of ideals of the etale structure sheaf of Noetherian schemes are provably not finitely generated. So the present tools will not interpret the etale cohomology of Noetherian schemes in second order arithmetic
Zariski cohomology in second order arithmetic
Colin McLarty
Abstract
The cohomology of coherent sheaves and sheaves of Abelian groups on Noetherian schemes are interpreted in second order arithmetic by means of a finiteness theorem. This finiteness theorem provably fails for the etale topology even on Noetherian schemes.