On the image of p -adic regulators

Abstract

Let V denote a complete discrete valuation ring with a fraction eld K of characteristic 0 and a perfect residue eld k of positive characteristic p, let V0 = W (k) denote the ring of Witt vectors with coe cients in k, and K0 its fraction eld. Set GK = Gal(K=K). Let X be a smooth and projective scheme over V . For i = 0, 2i − n− 1= 0, consider the Galois representation L = Hn et (XK ;Qp(i)). In the work of Bloch and Kato on the special values of L-functions of motives [2], the question of describing the images of the Soul e’s p-adic Chern character