dc.contributor.author
Fité, F.
dc.date.accessioned
2024-05-08T13:36:08Z
dc.date.accessioned
2024-09-19T14:25:17Z
dc.date.available
2024-05-08T13:36:08Z
dc.date.available
2024-09-19T14:25:17Z
dc.date.issued
2024-01-01
dc.identifier.uri
http://hdl.handle.net/2072/537585
dc.description.abstract
Let A be an abelian variety defined over a number field and of dimension g. When g ≤ 2, by the recent work of Sawin, we know the exact (nonzero) value of the density of the set of primes which are ordinary for A. In higher dimension very little is known. We show that if g = 3 and A has multiplication by an imaginary quadratic field E, then there exists a nonzero density set of ordinary primes for A. We reach the same conclusion if g = 4 and the pair (A, E) has signature (2, 2). We also obtain partial results when g = 3 and A has multiplication by a totally real cubic field. We show that our methods also apply to certain abelian varieties of Albert type IV of higher dimension. These results are derived from an extended version of the `-adic methods of Katz, Ogus, and Serre in the presence of extra endomorphisms. © 2024 Universitat Autonoma de Barcelona. All rights reserved.
eng
dc.description.sponsorship
Acknowledgements. Thanks to Bjorn Poonen for explaining the content of [8, Proposition 2.7.1] to the attendants of the MIT number theory group meeting. Thanks to Drew Sutherland for drawing my attention to the question considered in this note in the case of Picard curves. Thanks to Xavier Guitart for helpful discussions and for his comments and corrections to a previous version of this manuscript, as well as for alerting me to the existence of [17]. I was financially supported by the Simons Foundation grant 550033.
dc.description.sponsorship
This work has also being supported by the Spanish State Research Agency , through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D ( CEX2020-001084-M ).
dc.format.extent
14 p.
cat
dc.publisher
Universitat Autonoma de Barcelona
cat
dc.relation.ispartof
Publicacions Matematiques
cat
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Endomorphism algebras; ordinary abelian varieties; λ-adic representations
cat
dc.title
ORDINARY PRIMES FOR SOME VARIETIES WITH EXTRA ENDOMORPHISMS
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.identifier.doi
10.5565/PUBLMAT6812402
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
