### Abstract

Cech cohomology of Semiring schemes
Jaiung Jun (State University of New York at Binghamton, USA)) /
A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize Cech cohomology theory and invertible sheaves to semiring schemes. In particular, when X is a projective space over a totally ordered idempotent semifield M, we show that cohomology semimodules vanish as in the classical computation for all n. Finally, we classify all invertible sheaves on X by computing Pic(X) explicitly