Frobenius sign separation for abelian varieties
| Autor: | Bucur, Alina, Fité, Francesc, Kedlaya, Kiran S. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let A and A' be abelian varieties defined over a number field k such that Hom(A,A') = 0. Under the Generalized Riemann hypothesis for motivic L-functions attached to A and A', we show that there exists a prime p of k of good reduction for A and A' at which the Frobenius traces of A and A' are nonzero and differ by sign, and such that the norm Nm(p) is O(log(2NN')^2), where N and N' respectively denote the absolute conductors of A and A'. Our method extends that of Chen, Park, and Swaminathan who considered the case in which A and A' are elliptic curves. Comment: 9 pages. Includes material formerly appearing in arXiv:2002.08807 |
| Databáze: | arXiv |
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