Zariski cohomology in second order arithmetic

2012/07/02 by Colin McLarty, McLarty, Colin
Mathematics · #03F35 #14A99 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #msc:03F35 #msc:14A99

paper · pdf · doi:10.48550/arxiv.1207.0276

Besides 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

openalex publication_date 2012/07/02 · arxiv created 2012/07/25 · arxiv updated 2012/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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