The Infrastructure of a Global Field of Arbitrary Unit Rank

Details The Infrastructure of a Global Field of Arbitrary Unit Rank The Infrastructure of a Global Field of Arbitrary Unit Rank

2008-09-09

arxiv.org/abs/0809.1685v3

Math. Comp. 80 (2011), no. 276, 2325--2357

Mathematics

Number Theory

Revised version. Accepted for publication in Math. Comp

Scientific paper

10.1090/S0025-5718-2011-02490-7

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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