Pith. sign in

REVIEW 1 cited by

Equivariant vector bundles on toric schemes over semirings

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2406.06933 v1 pith:4PD4AS5Z submitted 2024-06-11 math.AG

Jaiung Jun , Kalina Mincheva , Jeffrey Tolliver This is my paper · ORCID
classification math.AG
keywords toricbundlesvectorequivariantidempotentproveschemessemifield
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric vector bundle on a toric scheme $X$ over an idempotent semifield equivariantly splits as a sum of toric line bundles. We then study the equivariant Picard group $\text{Pic}_G(X)$. Finally, we prove a version of Klyachko's classification theorem for toric vector bundles over an idempotent semifield.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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.

Pith tools