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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2603.12116 |
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| _version_ | 1866913021981360128 |
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| author | Muller, Joseph Yu, Chia-Fu |
| author_facet | Muller, Joseph Yu, Chia-Fu |
| contents | In this expository paper, given a field $K$ and two automorphisms $σ, τ\in \mathrm{Aut}(K)$, we give a self-contained proof of the classification of finite dimensional $K$-vector spaces equipped with two operators $F$ and $V$, respectively $σ$-linear and $τ$-linear, such that $FV = VF = 0$. This classification was originally due to the combined results of Gelfand and Ponomarev (1968), and of Kraft (1975). Following a recent suggestion of Chai (2025), we reworked their classification in light of the notion of Kraft quivers. As an application, we generalize and give an algebraic proof of a theorem by Kottwitz and Rapoport concerning the existence of $F$-crystals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12116 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Twisted Gelfand-Ponomarev modules Muller, Joseph Yu, Chia-Fu Representation Theory Commutative Algebra 16G20, 13E10, 14L15 In this expository paper, given a field $K$ and two automorphisms $σ, τ\in \mathrm{Aut}(K)$, we give a self-contained proof of the classification of finite dimensional $K$-vector spaces equipped with two operators $F$ and $V$, respectively $σ$-linear and $τ$-linear, such that $FV = VF = 0$. This classification was originally due to the combined results of Gelfand and Ponomarev (1968), and of Kraft (1975). Following a recent suggestion of Chai (2025), we reworked their classification in light of the notion of Kraft quivers. As an application, we generalize and give an algebraic proof of a theorem by Kottwitz and Rapoport concerning the existence of $F$-crystals. |
| title | Twisted Gelfand-Ponomarev modules |
| topic | Representation Theory Commutative Algebra 16G20, 13E10, 14L15 |
| url | https://arxiv.org/abs/2603.12116 |