Katz–Radon Transform of ℓ-Adic Representations

RECOVERING l - ADIC REPRESENTATIONS

We consider the problem of recovering l-adic representations from a knowledge of the character values at the Frobenius elements associated to l-adic representations constructed algebraically out of the original representations. These results generalize earlier results in [Ra] concerning refinements of strong multiplicity one for l-adic represntations, and a result of Ramakrishnan [DR] recoverin...

Abelian varieties, l-adic representations, and l-independence

In the case that K is a number field, this conjecture goes back almost thirty years. The Lie algebra analogue has been formulated by J. Tate [18], D. Mumford [10], and J.-P. Serre [13]. A more precise conjecture involves comparison with the singular homology group H1(A(C),Q) for a fixed embedding K ⊂ C. If G∞ denotes the associated Hodge group (cf. §4), the “Mumford-Tate” conjecture states that...

ON l-ADIC FAMILIES OF CUSPIDAL REPRESENTATIONS OF GL2(Qp)

We compute the universal deformations of cuspidal representations π of GL2(F ) over Fl, where F is a local field of residue characteristic p and l is an odd prime different from p. When π is supercuspidal there is an irreducible, two dimensional representation ρ of GF that corresponds to π via the mod l local Langlands correspondence of [Vi2]; we show that there is a natural isomorphism between...

Meromorphic Continuation of L-functions of P-adic Representations

Review of Abelian l-adic Representations and Elliptic Curves

Addison-Wesley has just reissued Serre’s 1968 treatise on l-adic representations in their Advanced Book Classics series. This circumstance presents a welcome excuse for writing about the subject, and for placing Serre’s book in a historical perspective. The theory of l-adic representations is an outgrowth of the study of abelian varieties in positive characteristic, which was initiated by Hasse...