arXiv 0809.16852008-09math.NT

The Infrastructure of a Global Field of Arbitrary Unit Rank

Felix Fontein

备注：: Revised version. Accepted for publication in Math. Comp
发表信息：: Math. Comp. 80 (2011), no. 276, 2325--2357
DOI：: 10.1090/S0025-5718-2011-02490-7

英文摘要：

In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant step operation and f-representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish that effective implementation of the presented methods is indeed possible, and we show how Shanks' baby-step giant-step method can be generalized to this situation.

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