L-functions of Φ-sheaves and Drinfeld Modules
نویسنده
چکیده
In this paper, we apply Dwork’s p-adic methods to study the meromorphic continuation and rationality of various L-functions arising from π-adic Galois representations, Drinfeld modules and φ-sheaves. As a consequence, we prove some conjectures of Goss about the rationality of the local L-function and the meromorphic continuation of the global L-function attached to a Drinfeld module. Let Fq be a finite field of q elements with characteristic p. Let π be a prime of the polynomial ring A = Fq[t]. Let Aπ be the completion of the ring A at π. This is an analogue of the classical ring Zp of p-adic integers. Let X be an irreducible algebraic variety defined over Fq and let π1(X) be the arithmetic fundamental group of X/Fq with respect to some base point. The group π1(X) may be regarded as the Galois group of a separable closure of the function field of X/Fq modulo the inertia groups at the closed points of X/Fq. Suppose now that we are given a continuous π-adic representation
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تاریخ انتشار 1996