GENERALIZED KUMMER CONGRUENCES

AND p-ADIC FAMILIES OF MOTIVES

Alexei A. Panchishkin

Abstract. We describe some new general constructions of p-adic L-functions attached to certain arithmetically defined complex L-functions coming from motives over Q with coefficiens in a number field T, with [T : Q] < ∞. These constructions are equivalent to proving some generalized Kummer congruences for critical special values of these complex L-functions.

Typeset by AMS-TEX