Motives, Periods, and Functoriality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909533128884224 |
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| author | Deligne, Pierre Raghuram, A. |
| author_facet | Deligne, Pierre Raghuram, A. |
| contents | Given a pure motive $M$ over $\mathbb{Q}$ with a multilinear algebraic structure $\mathsf{s}$ on $M$, and given a representation $V$ of the group respecting $\mathsf{s}$, we describe a functorial transfer $M^V$. We formulate a criterion that guarantees when the two periods of $M^V$ are equal. This has an implication for the critical values of the $L$-function attached to $M^V.$ The criterion is explicated in a variety of examples such as: tensor product motives and Rankin-Selberg $L$-functions; orthogonal motives and the standard $L$-function for even orthogonal groups; twisted tensor motives and Asai $L$-functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_03342 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Motives, Periods, and Functoriality Deligne, Pierre Raghuram, A. Number Theory Algebraic Geometry Representation Theory 11F67, 11G09, 22E55 Given a pure motive $M$ over $\mathbb{Q}$ with a multilinear algebraic structure $\mathsf{s}$ on $M$, and given a representation $V$ of the group respecting $\mathsf{s}$, we describe a functorial transfer $M^V$. We formulate a criterion that guarantees when the two periods of $M^V$ are equal. This has an implication for the critical values of the $L$-function attached to $M^V.$ The criterion is explicated in a variety of examples such as: tensor product motives and Rankin-Selberg $L$-functions; orthogonal motives and the standard $L$-function for even orthogonal groups; twisted tensor motives and Asai $L$-functions. |
| title | Motives, Periods, and Functoriality |
| topic | Number Theory Algebraic Geometry Representation Theory 11F67, 11G09, 22E55 |
| url | https://arxiv.org/abs/2403.03342 |