Abstract
In this text, we generalize Čech cohomology to sheaves 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,F) turn out to be blue B-modules. For a locally free OX-module F on a monoidal scheme X, we prove that Hl(X,F)+=Hl(X+,F+) where X+ is the scheme associated with X and F+ is the locally free OX+-module associated with 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 F1.
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