On $p$-adic $L$-functions Attached to Motives over $Q$

Unités cyclotomiques, unités semi-locales et ${\Bbb Z}_\ell$-extensions. II

“…aussi [16]) qui repose sur l'emploi des dérivées logarithmiques. L'objet du § 6 est de montrer que, comme dans le cas de Q(Ç^), le résultat précédent a des conséquences sur les groupes de classes : si L^ désigne la /-extension abélienne non ramifiée maximale de K^, il permet de traduire la conjecture de R. Greenberg, [10] (intermédiaire entre la conjecture principale de [2], § 5.1 et celle de Coates et Lichtenbaum, [3] conj. 2.3) portant sur la partie imaginaire de Gai (L^/K^) en un énoncé portant sur la partie réelle : énoncé qui est une version «à la limite projective » de la conjecture de G. Gras (cf.…”

Bounded p-adic L-functions of motives at supersingular primes

“…There exists a C p -meromorphic function L Remarks. (i) Conjecture 1 extends the conjecture of Coates and Perrin-Riou [3,4], where they have formulated such a conjecture if p is good ordinary for M. In this case, in particular, the p-Newton and Hodge polygons coincide. (ii) The condition in part (iii) of Conjecture 1 is called the condition of Dąbrowski-Panchishkin (see also [16]).…”

“…Let M be a pure motive over Q (with coefficients in Q, for simplicity) of weight w = w(M) and rank d = d(M), given by Betti, de Rham and l-adic realizations (for each prime l) H B (M), H D R (M) and H l (M) which are, respectively, vector spaces over Q, Q and Q l of dimension d, and which are endowed with the additional structures and comparison isomorphisms (for details see [8,4,3] in the sense of Deligne [8]) for some Dirichlet character χ and an integer m satisfying 0 = sign((−1) m (χ )). Deligne's period conjecture (see [8]) asserts that the quantity…”

Iwasawa Theory and Motivic L-functions

“…As demonstrated in [21, §4] the nonabelian conjectures of [13] (and also of [26]) are consequences of Conjecture 7. It is also shown in [21, §4] that the earlier conjectures of Coates and Perrin-Riou on the cyclotomic deformation of ordinary motives [10] follow from Conjecture 7.…”