Cech Cohomology of Semiring Schemes

A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize Čech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective space over a totally ordered idempotent semifield $M$, we show that Čech cohomology theory is in agreement with the classical computation. Finally, we classify all invertible sheaves on $X=\mathbb{P}^n_M$ by computing the Picard group of $X$ explicitly.

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