On some finiteness results in real étale cohomology. Issue 2 (17th March 2022)

• Record Type: Journal Article
• Authors: Jin, Fangzhou
• Is Part Of: Bulletin of the London Mathematical Society. Volume 54:Issue 2(2022)
• Page Start: 389
• Page End: 403
• Publication Date: 2022-03-17
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12563
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: We show that for quasi‐compact quasi‐separated schemes of finite dimension, the constructibility condition in real étale cohomology agrees with a notion of constructibility arising naturally from topology. As application we prove that the derived direct image functor preserves constructibility under some assumptions, and compute the Grothendieck group of the constructible rational stable motivic homotopy category for reasonable schemes. We prove the generic base change property for constructible real étale sheaves, and deduce the same property for rational motivic spectra and b ‐sheaves.