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A bound for the image conductor of a principally polarized abelian variety with open Galois image.
- Source :
-
Proceedings of the American Mathematical Society, Series B . 5/27/2022, Vol. 9, p272-285. 14p. - Publication Year :
- 2022
-
Abstract
- Let A be a principally polarized abelian variety of dimension g over a number field K. Assume that the image of the adelic Galois representation of A is an open subgroup of GSp_{2g}(\hat {\mathbb {Z}}). Then there exists a positive integer m so that the Galois image of A is the full preimage of its reduction modulo m. The least m with this property, denoted m_A, is called the image conductor of A. Jones [Pacific J. Math. 308 (2020), pp. 307–331] recently established an upper bound for m_A, in terms of standard invariants of A, in the case that A is an elliptic curve without complex multiplication. In this paper, we generalize the aforementioned result to provide an analogous bound in arbitrary dimension. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ELLIPTIC curves
*ABELIAN varieties
*MATHEMATICS
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 23301511
- Volume :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society, Series B
- Publication Type :
- Academic Journal
- Accession number :
- 157127474
- Full Text :
- https://doi.org/10.1090/bproc/131