Geometry & Topology Monographs 3 (2000) - Invitation to higher local fields, Part II, section 1, pages 199-213

Higher dimensional local fields and L-functions

A. N. Parshin

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.
Keywords. L-function, higher dimensional local fields, adelic complexes.
AMS subject classification. 14G99, 14G45, 11M99.

E-print: arXiv:math.NT/0012151

A. N. Parshin
Department of algebra, Steklov mathematical institute, ul. Gubkina 8, Moscow GSP-1, 117966 Russia

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