Quaternions, polarizations and class numbers
| dc.creator | Rotger, Victor | |
| dc.date | 2002-11-06 | |
| dc.date.accessioned | 2026-07-07T04:52:44Z | |
| dc.date.available | 2026-07-07T04:52:44Z | |
| dc.description | We study abelian varieties $A$ with multiplication by a totally indefinite quaternion algebra over a totally real number field and give a criterion for the existence of principal polarizations on them in pure arithmetic terms. Moreover, we give an expression for the number $π_0(A)$ of isomorphism classes of principal polarizations on $A$ in terms of relative class numbers of CM fields by means of Eichler's theory of optimal embeddings. As a consequence, we exhibit simple abelian varieties of any even dimension admitting arbitrarily many non-isomorphic principal polarizations. On the other hand, we prove that $π_0(A)$ is uniformly bounded for simple abelian varieties of odd square-free dimension. | |
| dc.description | To appear in Crelle | |
| dc.identifier | https://arxiv.org/abs/math/0211120 | |
| dc.identifier | http://arxiv.org/abs/math/0211120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65579 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Quaternions, polarizations and class numbers | |
| dc.type | text |