Witt invariants of Weyl groups
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916345199722496 |
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| author | Blanks, Tamar |
| author_facet | Blanks, Tamar |
| contents | We describe the Witt invariants of a Weyl group over a field $k_0$ by giving generators for the $W(k_0)$-module of Witt invariants, under the assumption that the characteristic of $k_0$ does not divide the order of the group. For the Weyl groups of types $B_n$, $C_n$, $D_n$, and $G_2$, we show that the Witt invariants are generated as a $W(k_0)$-algebra by trace forms and their exterior powers, extending a result due to Serre in type $A_n$. Many of our computational methods are applicable to computing Witt invariants of any smooth linear algebraic group over $k_0$, including a technique for lifting module generators from cohomological invariants to Witt invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07972 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Witt invariants of Weyl groups Blanks, Tamar Rings and Algebras Algebraic Geometry Number Theory 12G05, 11E04 We describe the Witt invariants of a Weyl group over a field $k_0$ by giving generators for the $W(k_0)$-module of Witt invariants, under the assumption that the characteristic of $k_0$ does not divide the order of the group. For the Weyl groups of types $B_n$, $C_n$, $D_n$, and $G_2$, we show that the Witt invariants are generated as a $W(k_0)$-algebra by trace forms and their exterior powers, extending a result due to Serre in type $A_n$. Many of our computational methods are applicable to computing Witt invariants of any smooth linear algebraic group over $k_0$, including a technique for lifting module generators from cohomological invariants to Witt invariants. |
| title | Witt invariants of Weyl groups |
| topic | Rings and Algebras Algebraic Geometry Number Theory 12G05, 11E04 |
| url | https://arxiv.org/abs/2309.07972 |