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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.18645 |
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| _version_ | 1866918075399405568 |
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| author | Borger, James Jun, Jaiung |
| author_facet | Borger, James Jun, Jaiung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Facets of module theory over semirings Borger, James Jun, Jaiung Algebraic Geometry 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. |
| title | Facets of module theory over semirings |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.18645 |