Frobenius Traces for Rank-2 Drinfeld Modules, Higher-Dimensional Galois Representations, and a Strong Multiplicity One Theorem in Positive Characteristic
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915975600799744 |
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| author | Chen, Chien-Hua |
| author_facet | Chen, Chien-Hua |
| contents | In this paper, we prove that if the Frobenius traces agree at all but finitely many places, then two $l$-adic Galois representations, associated to rank-$2$ non-CM Drinfeld modules of generic characteristic, are isomorphic. As a generalization, we show that the "Frobenius trace equality at all but finitely many places forces isomorphism" between two Galois representations over a local field of positive characteristic holds under an absolute irreducibility assumption. Moreover, we formulate and prove a function field analogue of strong multiplicity one property for semisimple Galois representations over a local field of positive characteristic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_28015 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frobenius Traces for Rank-2 Drinfeld Modules, Higher-Dimensional Galois Representations, and a Strong Multiplicity One Theorem in Positive Characteristic Chen, Chien-Hua Number Theory In this paper, we prove that if the Frobenius traces agree at all but finitely many places, then two $l$-adic Galois representations, associated to rank-$2$ non-CM Drinfeld modules of generic characteristic, are isomorphic. As a generalization, we show that the "Frobenius trace equality at all but finitely many places forces isomorphism" between two Galois representations over a local field of positive characteristic holds under an absolute irreducibility assumption. Moreover, we formulate and prove a function field analogue of strong multiplicity one property for semisimple Galois representations over a local field of positive characteristic. |
| title | Frobenius Traces for Rank-2 Drinfeld Modules, Higher-Dimensional Galois Representations, and a Strong Multiplicity One Theorem in Positive Characteristic |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.28015 |