Hecke Modules and Supersingular
نویسنده
چکیده
Let F be a nonarchimedean local field of odd residual characteristic p. We classify finite-dimensional simple right modules for the pro-pIwahori-Hecke algebra HC(G, I(1)), where G is the unramified unitary group U(2, 1)(E/F ) in three variables. Using this description when C = Fp, we define supersingular Hecke modules and show that the functor of I(1)-invariants induces a bijection between irreducible nonsupersingular mod-p representations of G and nonsupersingular simple right HC(G, I(1))-modules. We then use an argument of Paškūnas to construct supersingular representations of G.
منابع مشابه
Hecke Operators for Weakly Holomorphic Modular Forms and Supersingular Congruences
We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.
متن کاملDrinfeld Modules with No Supersingular Primes
We give examples of Drinfeld modules φ of rank 2 and higher over Fq(T ) that have no primes of supersingular reduction. The idea is to construct φ so that the associated mod ` representations are incompatible with the existence of supersingular primes. We also answer a question of Elkies by proving that such obstructions cannot exist for elliptic curves over number fields. Elkies [El1] proved t...
متن کاملHecke Algebras Acting on Elliptic Cohomology
Introduction. In our earlier papers [2,3,4,5,6], we investigated stable operations and cooperations in elliptic cohomology and its variants, relating these to known operations on rings of modular forms. The purpose of this article is to give an introduction to these stable operation algebras, in particular explaining the connections with Hecke algebras and Morava stabilizer algebras; further de...
متن کاملHecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms
In his letter (Serre, 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → Fp, where B is the endomorphism algebra of a supersingular elliptic curve. We generalize this result to Siegel modular forms, proving that the systems of Hecke eigenvalues given by Siegel modular forms (mod p)...
متن کاملON THE UNIVERSAL SUPERSINGULAR MOD p REPRESENTATIONS OF GL 2 ( F )
The irreducible supersingular mod p representations of G = GL2(F ), where F is a finite extension of Qp, are the building blocks of the mod p representation theory of G. They all arise as irreducible quotients of certain universal supersingular representations. We investigate the structure of these universal modules in the case when F/Qp is totally ramified.
متن کامل