Invitation to higher local fields, Part II, section 1: Higher dimensional local fields and L-functions

Details Invitation to higher local fields, Part II, section 1: Higher dimensional local fields and L-functions Invitation to higher local fields, Part II, section 1: Higher dimensional local fields and L-functions

2000-12-18

arxiv.org/abs/math/0012151v1

Geom. Topol. Monogr. Volume 3(2000) 199-213

Mathematics

Number Theory

For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwi

Scientific paper

This work describes several first steps in extending Tate-Iwasawa's analytic method to define an L-function in higher dimensions. For generalizing this method the author advocates the usefulness of the classical Riemann-Hecke approach, his adelic complexes together with his generalization of Krichever's correspondence. He analyzes dimension 1 types of functions and discusses properties of the lattice of commensurable classes of subspaces in the adelic space associated to a divisor on an algebraic surface.

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