Publications Mathématiques de Besançon

Algèbre et Théorie des Nombres
no. 1
Weight reduction for cohomological mod p modular forms over imaginary quadratic fields
Adam Mohamed1
1 Universität Duisburg-Essen, Institut für Experimentelle Mathematik, Ellernstr 29, 45326 Essen, Germany
Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2014), pp. 45-71.

Soient F un corps quadratique imaginaire et 𝒪 son anneau d’entiers. Soient 𝔫⊂𝒪 un idéal non nul et p>5 un nombre premier inerte dans F copremier avec 𝔫. Soit V une représentation irréductible de dimension finie de 𝔽 ¯ p [ GL 2 (𝔽 p 2 )]. Nous établissons qu’un système de valeurs propres de Hecke appartenant au groupe de cohomologie â ?¡ coefficients dans V appartient aussi au groupe de cohomologie â ?¡ coefficients dans 𝔽 ¯ p ⊗det e pour e≥0 à l’exception, éventuellement, de quelques cas.

Let F be an imaginary quadratic field and 𝒪 its ring of integers. Let 𝔫⊂𝒪 be a non-zero ideal and let p>5 be a rational inert prime in F and coprime with 𝔫. Let V be an irreducible finite dimensional representation of 𝔽 ¯ p [ GL 2 (𝔽 p 2 )]. We establish that a system of Hecke eigenvalues appearing in the cohomology with coefficients in V already lives in the cohomology with coefficients in 𝔽 ¯ p ⊗det e for some e≥0; except possibly in some few cases.

Reçu le :
Publié le :
DOI : 10.5802/pmb.4
Classification : 11F75, 11F67, 11F25, 11F41
Mots clés : Modular forms modulo $p$, imaginary quadratic fields, Hecke operators, Serre weight
Adam Mohamed 1

1 Universität Duisburg-Essen, Institut für Experimentelle Mathematik, Ellernstr 29, 45326 Essen, Germany 
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Adam Mohamed. Weight reduction for cohomological mod $p$ modular forms over imaginary quadratic fields. Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 1 (2014), pp. 45-71. doi : 10.5802/pmb.4. https://pmb.centre-mersenne.org/articles/10.5802/pmb.4/

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