Invitation to higher local fields, Part II, section 1: Higher dimensional local fields and L-functions
Number Theory
2009-09-25 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0012151,
title = {Invitation to higher local fields, Part II, section 1: Higher dimensional local fields and L-functions},
author = {A. N. Parshin},
journal= {arXiv preprint arXiv:math/0012151},
year = {2009}
}
Comments
For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon3/m3-II-1.abs.html