Čech cohomology over 𝔽12
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Citation (published version)Jaret Flores, Oliver Lorscheid, Matt Szczesny. 2017. "Čech cohomology over 𝔽12." Journal of Algebra, Volume 485, pp. 269 - 287.
In this text, we generalize Cech cohomology to sheaves 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,) turn out to be blue B-modules. For locally free X-module on a monoidal scheme X, we prove that Hl(X,)+=Hl(X+,+) where X+ is the scheme associated with X and + is the locally free X+-module associated with . In an appendix, we show that the naive generalization of cohomology as a right derived functor is infinite-dimensional for the projective line over 𝔽1.