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ISSN 1088-6850(e) ISSN 0002-9947(p)

Geometry of Fermat adeles

Author(s): Alexandru Buium
Journal: Trans. Amer. Math. Soc. 357 (2005), 901-964.
MSC (2000): Primary 11G05, 11G30
Posted: October 19, 2004
MathSciNet review: 2110426
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Abstract: If $L(a,s):=\sum_n c(n,a)n^{-s}$ is a family of ``geometric'' functions depending on a parameter , then the function $(p,a)\mapsto c(p,a)$ , where runs through the set of prime integers, is not a rational function and hence is not a function belonging to algebraic geometry. The aim of the paper is to show that if one enlarges algebraic geometry by ``adjoining a Fermat quotient operation'', then the functions become functions in the enlarged geometry at least for functions of curves and Abelian varieties.

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