• Corpus ID: 254018401

# Les conjectures de Weil : origines, approches, g\'en\'eralisations

@inproceedings{ChambertLoir2022LesCD,
title={Les conjectures de Weil : origines, approches, g\'en\'eralisations},
author={Antoine Chambert-Loir},
year={2022}
}
The Weil conjectures: origins, approaches, generalizations) I recount the history of the conjectures by Weil on the number of solutions of polynomial equations in finite fields, and some of the approaches that have been proposed to solve them.

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The statement of the Riemann hypothesis makes sense for all global fields, not just the rational numbers. For function fields, it has a natural restatement in terms of the associated curve. Weil's
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Smooth projective varieties $X$ over a finite field $k$ with $CH_0(X\otimes \bar{k(X)})=\mathbb Z$ have a rational point, in particular Fano varieties. We also refer to this http URL where the last
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The classical Riemann Hypothesis RH is among the most prominent unsolved problems in modern mathematics. The development of Number Theory in the 19th century spawned an arithmetic theory of
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Such equations have an interesting history. In art. 358 of the Disquisitiones [1, a], Gauss determines the Gaussian sums (the so-called cyclotomic “periods”) of order 3, for a prime of the form p =
ALGEBRAIC geometry, in spite of its beauty and importance, has long been reproached for lacking proper foundations. Great discoveries have been made, especially in Italy, by the intuition of a number
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