Cech Cohomology of Semiring Schemes

2015/03/04 by Jun, Jaiung · 1 citation
#14T99 #18G60 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.01389

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=ℙⁿ_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=ℙⁿ_M by computing the Picard group of X explicitly.

Cited by

• Radical-Ideal Functors, a Support Bifibration, and Quantale Completion for Commutative Semirings

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