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Facets of module theory over semirings

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arxiv 2405.18645 v3 pith:NDNO3NZI submitted 2024-05-28 math.AG

James Borger , Jaiung Jun This is my paper · ORCID
classification math.AG
keywords semiringstheoryagreebundledefinitionsgroupmoduleusual
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We set up some basic module theory over semirings, with particular attention to what is needed in scheme theory over semirings. We show that while not all the usual definitions of vector bundle agree over semirings, all the usual definitions of line bundle do agree. We also show that the narrow class group of a number field can be recovered as a reflexive Picard group of its subsemiring of totally nonnegative algebraic integers.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Representation theory over semifields

    math.RT 2024-11 conditional novelty 8.0 of 10

    For a finite or torsion group G over an idempotent semifield, representations are in one-to-one correspondence with G-sets.

  2. Tropical representations and valuated matroids

    math.RT 2024-11 conditional novelty 7.0 of 10

    Tropical subrepresentations of finite groups correspond exactly to weak isomorphism classes of weak group actions on valuated matroids.

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