On endomorphisms of extensions in Tannakian categories
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910704700751872 |
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| author | Eskandari, Payman |
| author_facet | Eskandari, Payman |
| contents | We prove some analogues of Schur's lemma for endomorphisms of extensions in Tannakian categories. More precisely, let $\mathbf{T}$ be a neutral Tannakian category over a field of characteristic zero. Let $E$ be an extension of $A$ by $B$ in $\mathbf{T}$. We consider conditions under which every endomorphism of $E$ that stabilizes $B$ induces a scalar map on $A\oplus B$. We give a result in this direction in the general setting of arbitrary $\mathbf{T}$ and $E$, and then a stronger result when $\mathbf{T}$ is filtered and the associated graded objects to $A$ and $B$ satisfy some conditions. We also discuss the sharpness of the results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06817 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On endomorphisms of extensions in Tannakian categories Eskandari, Payman Algebraic Geometry Number Theory Representation Theory 18M25 (primary), 08A35, 14F42 (secondary) We prove some analogues of Schur's lemma for endomorphisms of extensions in Tannakian categories. More precisely, let $\mathbf{T}$ be a neutral Tannakian category over a field of characteristic zero. Let $E$ be an extension of $A$ by $B$ in $\mathbf{T}$. We consider conditions under which every endomorphism of $E$ that stabilizes $B$ induces a scalar map on $A\oplus B$. We give a result in this direction in the general setting of arbitrary $\mathbf{T}$ and $E$, and then a stronger result when $\mathbf{T}$ is filtered and the associated graded objects to $A$ and $B$ satisfy some conditions. We also discuss the sharpness of the results. |
| title | On endomorphisms of extensions in Tannakian categories |
| topic | Algebraic Geometry Number Theory Representation Theory 18M25 (primary), 08A35, 14F42 (secondary) |
| url | https://arxiv.org/abs/2306.06817 |