Abstract
We saw in Chap. 25 that since his student years, Weil was very interested in the analogies between arithmetic and classical algebraic geometry. That is, between the study of the sets of solutions of systems of Diophantine equations and that of algebraic varieties defined over the field of complex numbers. His most famous paper in this direction is probably [184], published in 1949. He formulated there several conjectures relating geometry over complex numbers and over finite fields, which we now reproduce
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R. Hartshorne, Algebraic Geometry (Springer, New York, 1977)
M. Hindry, La preuve par André Weil de l’hypothèse de Riemann pour une courbe sur un corps fini, in Henri Cartan and André Weil mathématiciens du XX e siècle. Actes des Journées X-UPS 2012 (Éditions de l’École Polytechnique, Palaiseau, 2012), pp. 63–98
C. Houzel, La géométrie algébrique. Recherches historiques. (Librairie Scientifique et Technique A. Blanchard, Paris, 2002)
A. Weil, Numbers of solutions of equations in finite fields. Bull. Am. Math. Soc. (VI) 55, 497–508 (1949). Republished in Œuvres scientifiques I (Springer, New York, 1979), pp. 399–410
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Popescu-Pampu, P. (2016). Weil’s Conjectures. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_43
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DOI: https://doi.org/10.1007/978-3-319-42312-8_43
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