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
Email: parshin@mi.ras.ru
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