A CLASS OF p-ADIC GALOIS REPRESENTATIONS ARISING FROM ABELIAN VARIETIES OVER Qp
نویسنده
چکیده
Let V be a p-adic representation of the absolute Galois group G of Qp that becomes crystalline over a finite tame extension, and assume p 6= 2. We provide necessary and sufficient conditions for V to be isomorphic to the p-adic Tate module Vp(A) of an abelian variety A defined over Qp. These conditions are stated on the filtered (φ,G)module attached to V . 2000 Mathematics Subject Classification: Primary 14F30, 11G10; Secondary 11F80, 14G20, 14F20.
منابع مشابه
Lifting Galois Representations, and a Conjecture of Fontaine and Mazur
Mumford has constructed 4-dimensional abelian varieties with trivial endomorphism ring, but whose Mumford–Tate group is much smaller than the full symplectic group. We consider such an abelian variety, defined over a number field F , and study the associated p-adic Galois representation. For F sufficiently large, this representation can be lifted to Gm(Qp)× SL2(Qp) . Such liftings can be used t...
متن کاملFiltered Modules Corresponding to Potentially Semi-stable Representations
We classify the filtered modules with coefficients corresponding to two-dimensional potentially semi-stable p-adic representations of the Galois groups of p-adic fields under the assumptions that p is odd and the coefficients are large enough. Introduction Let p be an odd prime number, and let K be a p-adic field. The absolute Galois group of K is denoted by GK . By the fundamental theorem of C...
متن کاملAnalytic vectors in continuous p-adic representations
Given a compact p-adic Lie group G over a finite unramified extension L/Qp let GL/Qp be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic GL/Qp -representations that coincides with passage to analytic vectors in case L = Qp. On the other hand, we study the functor ”passage to an...
متن کاملTHE CONJECTURE OF TATE AND VOLOCH ON p-ADIC PROXIMITY TO TORSION
Tate and Voloch have conjectured that the p-adic distance from torsion points of semi-abelian varieties over Cp to subvarieties may be uniformly bounded. We prove this conjecture for torsion points on semi-abelian varieties over Qp using methods of algebraic model theory and a result of Sen on Galois representation of Hodge-Tate type. As a generalization of their theorem on linear forms in p-ad...
متن کامل’ HOMOMORPHISMS OF l - ADIC GALOIS GROUPS AND ABELIAN VARIETIES
Let k be a totally real field, and let A/k be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphisms are all defined over k. Then the only strictly compatible families of abstract, absolutely irreducible representations of Gal(k/k) coming from A are tensor products of Tate twists of symmetric powers of two-dimensional λ-adic representations plus field a...
متن کامل