Cech Cohomology of Semiring Schemes

Abstract

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 $X={\mathbb{P}}_M^n$, 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 $X={\mathbb{P}}_M^n$ by computing the Picard group of $X$ explicitly.

14 pages, Section 4 is rewritten with more general results

References in corpus (1)

• On exactness of long sequences of homology semimodules

Cited by in corpus (1)

• Toward Homological Characterization of Semirings by e-Injective Semimodules