Conjectures and results on modular representations of GL n (K) for a p-adic field K
Résumé
Let p be a prime number and K a finite extension of Qp. We state conjectures on the smooth representations of GLn(K) that occur in spaces of mod p automorphic forms (for compact unitary groups). In particular, when K is unramified, we conjecture that they are of finite length and predict their internal structure (extensions, form of subquotients) from the structure of a certain algebraic representation of GLn. When n = 2 and K is unramified, we prove several cases of our conjectures, including new finite length results.
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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