SOME BOUNDS FOR RAMIFICATION OF p-TORSION SEMI-STABLE REPRESENTATIONS
نویسندگان
چکیده
Let p be an odd prime, K a finite extension of Qp, GK = Gal(K̄/K) its absolute Galois group and e = e(K/Qp) its absolute ramification index. Suppose that T is a p-torsion representation of GK that is isomorphic to a quotient of GK -stable Zp-lattices in a semi-stable representation with HodgeTate weights {0, . . . , r}. We prove that there exists a constant μ depending only on n, e and r such that the upper numbering ramification group G (μ) K acts on T trivially.
منابع مشابه
On a Ramification Bound of Torsion Semi-stable Representations over a Local Field
Let p be a rational prime, k be a perfect field of characteristic p, W = W (k) be the ring of Witt vectors, K be a finite totally ramified extension of Frac(W ) of degree e and r be a non-negative integer satisfying r < p − 1. In this paper, we prove the upper numbering ramification group G (j) K for j > u(K, r, n) acts trivially on the p-torsion semi-stable GK-representations with Hodge-Tate w...
متن کاملOn a Ramification Bound of Semi-stable Torsion Representations over a Local Field
Let p be a rational prime, k be a perfect field of characteristic p, W = W (k) be the ring of Witt vectors, K be a finite totally ramified extension of Frac(W ) of degree e and r be a nonnegative integer satisfying r < p− 1. Let V be a semi-stable p-adic GK representation with Hodge-Tate weights in {0, . . . , r}. In this paper, we prove the upper numbering ramification group G (j) K for j > u(...
متن کاملBounds for the Torsion of Elliptic Curves over Extensions with Bounded Ramification
Let K be a number field and let E/K be an elliptic curve. The Mordell-Weil Theorem states that E(K), the set of K-rational points on E, can be given the structure of a finitely generated abelian group. In this note we consider elliptic curves defined over the rationals Q and provide bounds for the size of E(K)Tors, where K is an algebraic Galois extension of Q. Theorem 1. Let E/Q be an elliptic...
متن کاملON A RAMIFICATION BOUND OF SEMI-STABLE MOD p REPRESENTATIONS OVER A LOCAL FIELD
Let p be a rational prime, k be a perfect field of characteristic p, W = W (k) be the ring of Witt vectors, K be a finite totally ramified extension of Frac(W ) of degree e and r be a non-negative integer satisfying r < p − 1. In this paper, we prove the upper numbering ramification group G (j) K for j > 1+e(1+r/(p−1)) acts trivially on the mod p representations associated to the semi-stable p-...
متن کاملSurvey of Kisin’s Paper Crystalline
In p-adic Hodge theory there are fully faithful functors from certain categories of p-adic representations of the Galois group GK := Gal(K/K) of a p-adic field K to certain categories of semi-linear algebra structures on finite-dimensional vector spaces in characteristic 0. For example, semistable representations give rise to weakly admissible filtered (φ,N)-modules, and Fontaine conjectured th...
متن کامل