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Motivic p-adic L-functions. (English) Zbl 0725.11029
L-functions and arithmetic, Proc. Symp., Durham/UK 1989, Lond. Math. Soc. Lect. Note Ser. 153, 141-172 (1991).
[For the entire collection see Zbl 0718.00005.]
In this article, the author gives a conjectural description of the p-adic L-functions of a motive M, defined over \({\mathbb{Q}}\) and with coefficients in a number field K, and which has good ordinary reduction at the prime p. The main definitions for the theory of the complex L-function attached to M as well as the notion of p-adic pseudo measure are recalled. The author modifies the Euler factors of both finite and infinite primes and proposes a modified version of Deligne’s period conjecture. In this way, the formulation of the existence of the p-adic L-functions attached to M and their holomorphy properties appear in a more natural setting.

MSC:
11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
11S40 Zeta functions and \(L\)-functions
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)