2015/11/21 by Jaret Flores, Flores, Jaret, Matt Szczesny +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.1511.06875
14 pages
arxiv created 2015/11/21 · openalex publication_date 2015/11/21 · arxiv updated 2015/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this text, we generalize Cech cohomology to sheaves \mathcal F with values in blue B-modules where B is a blueprint with -1. If X is an object of the underlying site, then the cohomology sets Hl(X,\mathcal F) turn out to be blue B-modules. For locally free \mathcal OX-module \mathcal F on a monoidal scheme X, we prove that Hl(X,\mathcal F)+=Hl(X+,\mathcal F+) where X+ is the scheme associated with X and \mathcal F+ is the locally free \mathcal OX+-module associated with \mathcal F. In an appendix, we show that the naive generalization of cohomology as a right derived functor is infinite-dimensional for the projective line over \mathbb F1.