Weil representations associated to isocrystals over function fields
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914055403339776 |
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| author | Mornev, Maxim Pink, Richard |
| author_facet | Mornev, Maxim Pink, Richard |
| contents | Every Anderson $A$-motive $M$ over a field determines a compatible system of Galois representations on its Tate modules at almost all primes of $A$. This adapts easily to $F$-isocrystals, which are rational analogues of $A$-motives for the global function field $F:=\operatorname{Quot}(A)$. We extend this compatible system by constructing a Weil group representation associated to $M$ for every place of $F$. To this end we generalize the Tate module construction to a tensor functor on $F_{\mathfrak{p}}$-isocrystals that are not necessarily pure. To prove that this yields a compatible system, we work out how that construction behaves under reduction of $M$. As an offshoot we obtain a new kind of $\wp$-adic Weil representations associated to Drinfeld modules of special characteristic $\wp$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_20807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weil representations associated to isocrystals over function fields Mornev, Maxim Pink, Richard Number Theory 11G09, 11F80 Every Anderson $A$-motive $M$ over a field determines a compatible system of Galois representations on its Tate modules at almost all primes of $A$. This adapts easily to $F$-isocrystals, which are rational analogues of $A$-motives for the global function field $F:=\operatorname{Quot}(A)$. We extend this compatible system by constructing a Weil group representation associated to $M$ for every place of $F$. To this end we generalize the Tate module construction to a tensor functor on $F_{\mathfrak{p}}$-isocrystals that are not necessarily pure. To prove that this yields a compatible system, we work out how that construction behaves under reduction of $M$. As an offshoot we obtain a new kind of $\wp$-adic Weil representations associated to Drinfeld modules of special characteristic $\wp$. |
| title | Weil representations associated to isocrystals over function fields |
| topic | Number Theory 11G09, 11F80 |
| url | https://arxiv.org/abs/2507.20807 |