Let X be the projective line minus 0; 1; and N over Q p : The aim of the following is to give a series representations of the p-adic multi-zeta values in the depth two quotient. The approach is to use the liftingFðzÞ ¼ z p of the frobenius which is not a good choice near 1, but which gives simple formulas away from 1, and to relate the action of frobenius on the de Rham path from 0 to N and on the one from 0 to 1. Also some relations between the p-adic multi-zeta values of depth two are obtained. r 2004 Elsevier Inc. All rights reserved.
Abstract. For a number field, we have a Tannaka category of mixed Tate motives at our disposal. We construct p-adic points of the associated Tannaka group by using p-adic Hodge theory. Extensions of two Tate objects yield functions on the Tannaka group, and we show that evaluation at our p-adic points is essentially given by the inverse of the Bloch-Kato exponential map.
Abstract. We prove that the algebra of p-adic multi-zeta values, as defined in [4] or [2], are contained in another algebra which is defined explicitly in terms of series. The main idea is to truncate certain series, expand them in terms of series all of which are divergent except one, and then take the limit of the convergent one. The main result is Theorem 3.0.27.
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