Theta lifts of Bianchi modular forms and applications to paramodularity

We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the...

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Publicado: 2014
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246107_v92_n2_p353_Berger
http://hdl.handle.net/20.500.12110/paper_00246107_v92_n2_p353_Berger
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00246107_v92_n2_p353_Berger
record_format dspace
spelling paper:paper_00246107_v92_n2_p353_Berger2023-06-08T14:52:31Z Theta lifts of Bianchi modular forms and applications to paramodularity We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the non-vanishing result of Takeda. As an application of our lifting result, we exhibit an abelian surface B defined over Q, which is not a restriction of scalars of an elliptic curve and satisfies the paramodularity Conjecture of Brumer and Kramer. 2015 London Mathematical Society. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246107_v92_n2_p353_Berger http://hdl.handle.net/20.500.12110/paper_00246107_v92_n2_p353_Berger
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the non-vanishing result of Takeda. As an application of our lifting result, we exhibit an abelian surface B defined over Q, which is not a restriction of scalars of an elliptic curve and satisfies the paramodularity Conjecture of Brumer and Kramer. 2015 London Mathematical Society.
title Theta lifts of Bianchi modular forms and applications to paramodularity
spellingShingle Theta lifts of Bianchi modular forms and applications to paramodularity
title_short Theta lifts of Bianchi modular forms and applications to paramodularity
title_full Theta lifts of Bianchi modular forms and applications to paramodularity
title_fullStr Theta lifts of Bianchi modular forms and applications to paramodularity
title_full_unstemmed Theta lifts of Bianchi modular forms and applications to paramodularity
title_sort theta lifts of bianchi modular forms and applications to paramodularity
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246107_v92_n2_p353_Berger
http://hdl.handle.net/20.500.12110/paper_00246107_v92_n2_p353_Berger
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