Vectorial Drinfeld modular forms over Tate algebras

Abstract : In this text, we develop the theory of vectorial modular forms with values in Tate algebras introduced by the first author, in a very special case (dimension two, for a very particular representation of Γ := GL 2 (Fq[θ])). Among several results that we prove here, we determine the complete structure of the modules of these forms, we describe their specializations at roots of unity and their connection with Drinfeld modular forms for congruence subgroups of Γ and we prove that the modules generated by these forms are stable under the actions of Hecke operators.
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Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01293564
Contributeur : Federico Pellarin <>
Soumis le : vendredi 25 mars 2016 - 08:17:16
Dernière modification le : mardi 29 mars 2016 - 21:48:48
Document(s) archivé(s) le : dimanche 26 juin 2016 - 15:22:52

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  • HAL Id : hal-01293564, version 1
  • ARXIV : 1603.07914

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F Pellarin, R Perkins. Vectorial Drinfeld modular forms over Tate algebras. 2016. 〈hal-01293564〉

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