Commentary on “Numbers of solutions of equations in finite fields” by André Weil
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Abstract:
Immediately following the commentary below, this previously published article is reprinted in its entirety: André Weil, “Numbers and solutions of equations in finite fields”, Bull. Amer. Math. Soc., 55 (1949), no. 5, 497–508.References
- Théorie des topos et cohomologie étale des schémas. Tome 1: Théorie des topos, Lecture Notes in Mathematics, Vol. 269, Springer-Verlag, Berlin-New York, 1972 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4); Dirigé par M. Artin, A. Grothendieck, et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. MR 0354652
- Pierre Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273–307 (French). MR 340258, DOI 10.1007/BF02684373
- Pierre Deligne, Formes modulaires et représentations $l$-adiques, Séminaire Bourbaki. Vol. 1968/69: Exposés 347–363, Lecture Notes in Math., vol. 175, Springer, Berlin, 1971, pp. Exp. No. 355, 139–172 (French). MR 3077124
- P. Deligne, Cohomologie étale, Lecture Notes in Mathematics, vol. 569, Springer-Verlag, Berlin, 1977 (French). Séminaire de géométrie algébrique du Bois-Marie SGA $4\frac {1}{2}$. MR 463174, DOI 10.1007/BFb0091526
- J. Dieudonné, On the history of the Weil conjectures, in Etale Cohomology and the Weil Conjecture edited by E. Freitag and R. Kiehl, Ergeb. 13, Springer Verlag, N.Y., 1987.
- Bernard Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math. 82 (1960), 631–648. MR 140494, DOI 10.2307/2372974
- Alexander Grothendieck, The cohomology theory of abstract algebraic varieties, Proc. Internat. Congress Math. 1958., Cambridge Univ. Press, New York, 1960, pp. 103–118. MR 0130879
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
- Nicholas M. Katz, An overview of Deligne’s proof of the Riemann hypothesis for varieties over finite fields, Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974) Amer. Math. Soc., Providence, R.I., 1976, pp. 275–305. MR 0424822
- James S. Milne, The Riemann hypothesis over finite fields from Weil to the present day, The legacy of Bernhard Riemann after one hundred and fifty years. Vol. II, Adv. Lect. Math. (ALM), vol. 35, Int. Press, Somerville, MA, 2016, pp. 487–565. MR 3525903
- Frans Oort, The Weil conjectures, Nieuw Arch. Wiskd. (5) 15 (2014), no. 3, 211–219. MR 3243075
- Jean-Pierre Serre, Sur la topologie des variétés algébriques en caractéristique $p$, Symposium internacional de topología algebraica International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 24–53 (French). MR 0098097
- André Weil, Numbers of solutions of equations in finite fields, Bull. Amer. Math. Soc. 55 (1949), 497–508. MR 29393, DOI 10.1090/S0002-9904-1949-09219-4
- André Weil, Abstract versus classical algebraic geometry, Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, vol. III, Erven P. Noordhoff N. V., Groningen; North-Holland Publishing Co., Amsterdam, 1956, pp. 550–558. MR 0092196
- The Weil Conjectures, Wikipedia. Retrieved March 10, 2018.
Additional Information
- Mark Goresky
- Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey
- MR Author ID: 75495
- Email: goresky@ias.edu
- Received by editor(s): March 16, 2018
- Published electronically: April 3, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 55 (2018), 327-329
- MSC (2010): Primary 11G25, 11M38, 14F20
- DOI: https://doi.org/10.1090/bull/1617
- MathSciNet review: 3803154