Abstract
In the last few years, it has become increasingly evident that the study of the zeta-function of an algebraic variety can yield valuable information about that variety, some of which cannot easily be obtained in any other way. Most of this information is number-theoretic — that is to say, it refers to objects which depend on the ground field and which are only of interest when the ground field is finitely generated. But some of it refers to objects, such as the Néron-Severi group, which are also of interest to classical algebraic geometers — and about which classical algebraic geometry has little to say.
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Swinnerton-Dyer, P. (1967). The Conjectures of Birch and Swinnerton-Dyer, and of Tate. In: Springer, T.A. (eds) Proceedings of a Conference on Local Fields. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87942-5_11
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