arXiv math/00121512000-12-18math.NTmath.AG

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

A. N. Parshin

备注：: 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
发表信息：: Geom. Topol. Monogr. Volume 3(2000) 199-213

英文摘要：

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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