Examples of genuine QM abelian surfaces which are modular View Full Text


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Article Info

DATE

2019-03

AUTHORS

Ciaran Schembri

ABSTRACT

Let K be an imaginary quadratic field. Modular forms for GL(2) over K are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational Bianchi newform has either an associated elliptic curve over K or an associated abelian surface with quaternionic multiplication over K. We give explicit evidence in the way of examples to support this conjecture in the latter case. Furthermore, the quaternionic surfaces given correspond to genuine Bianchi newforms, which answers a question posed by Cremona as to whether this phenomenon can happen. More... »

PAGES

11

References to SciGraph publications

  • 1973-12. On an analogue of the Sato conjecture in INVENTIONES MATHEMATICAE
  • 2003. The Arithmetic of Hyperbolic 3-Manifolds in NONE
  • 1993-12. l-adic representations associated to modular forms over imaginary quadratic fields in INVENTIONES MATHEMATICAE
  • 1994-12. l-adic representations associated to modular forms over imaginary quadratic fields. II in INVENTIONES MATHEMATICAE
  • 1972-09. On the arithmetic of abelian varieties in INVENTIONES MATHEMATICAE
  • 1995. Representations of Galois Groups Associated to Modular Forms in PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS
  • Journal

    TITLE

    Research in Number Theory

    ISSUE

    1

    VOLUME

    5

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40993-018-0150-x

    DOI

    http://dx.doi.org/10.1007/s40993-018-0150-x

    DIMENSIONS

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