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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2109.11961 |
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| _version_ | 1866912574884282368 |
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| author | Forey, Arthur Fresán, Javier Kowalski, Emmanuel |
| author_facet | Forey, Arthur Fresán, Javier Kowalski, Emmanuel |
| contents | We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we construct a tannakian category with convolution as tensor operation. Using Deligne's Riemann Hypothesis, we show how this leads to a general equidistribution theorem for the discrete Fourier transforms of trace functions of perverse sheaves, generalizing the work of Katz in the case of the multiplicative group. We then give some concrete examples of applications of these results and raise a number of questions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_11961 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution Forey, Arthur Fresán, Javier Kowalski, Emmanuel Number Theory Algebraic Geometry 11LXX, 11T23, 14F20, 18N25 We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we construct a tannakian category with convolution as tensor operation. Using Deligne's Riemann Hypothesis, we show how this leads to a general equidistribution theorem for the discrete Fourier transforms of trace functions of perverse sheaves, generalizing the work of Katz in the case of the multiplicative group. We then give some concrete examples of applications of these results and raise a number of questions. |
| title | Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution |
| topic | Number Theory Algebraic Geometry 11LXX, 11T23, 14F20, 18N25 |
| url | https://arxiv.org/abs/2109.11961 |