Quadratic enrichment of the logarithmic derivative of the zeta function
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866929402961461248 |
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| author | Bilu, Margaret Ho, Wei Srinivasan, Padmavathi Vogt, Isabel Wickelgren, Kirsten |
| author_facet | Bilu, Margaret Ho, Wei Srinivasan, Padmavathi Vogt, Isabel Wickelgren, Kirsten |
| contents | We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck--Witt group. We show that this enrichment is related to the topology of the real points of a lift. For cellular schemes over a field, we prove a rationality result for this enriched logarithmic derivative of the zeta function as an analogue of part of the Weil conjectures. We also compute several examples, including toric varieties, and show that the enrichment is a motivic measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_03035 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quadratic enrichment of the logarithmic derivative of the zeta function Bilu, Margaret Ho, Wei Srinivasan, Padmavathi Vogt, Isabel Wickelgren, Kirsten Algebraic Geometry Algebraic Topology K-Theory and Homology Number Theory Primary 14G10, 14F42, Secondary 19D45, 55P25, 11G25 We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck--Witt group. We show that this enrichment is related to the topology of the real points of a lift. For cellular schemes over a field, we prove a rationality result for this enriched logarithmic derivative of the zeta function as an analogue of part of the Weil conjectures. We also compute several examples, including toric varieties, and show that the enrichment is a motivic measure. |
| title | Quadratic enrichment of the logarithmic derivative of the zeta function |
| topic | Algebraic Geometry Algebraic Topology K-Theory and Homology Number Theory Primary 14G10, 14F42, Secondary 19D45, 55P25, 11G25 |
| url | https://arxiv.org/abs/2210.03035 |