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Uva-DARE (Digital Academic Repository) UvA-DARE (Digital Academic Repository) Optimality properties of curves over finite fields Zaitsev, A.I. Publication date 2008 Link to publication Citation for published version (APA): Zaitsev, A. I. (2008). Optimality properties of curves over finite fields. Thomas Stieltjes Institute for Mathematics. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:27 Sep 2021 Bibliography [1] Aldo Andreotti. On a theorem of Torelli. Amer.J.Math., 80:801–828, 1958. [2] Juscelino Bezerra, Arnaldo Garcia, and Henning Stichtenoth. An explicit tower of function fields over cubic finite fields and Zink’s lower bound. J. Reine Angew. Math., 589:159–199, 2005. [3] Pierre Deligne. Vari´et´es ab´eliennes ordinaires sur un corps fini. Invent. Math., 8:238–243, 1969. [4] Max Deuring. Die Typen der Multiplikatorenringe elliptischer Funktio- nenk¨orper. Abh. Math. Sem. Hansischen Univ., 14:197–272, 1941. [5] Noam D. Elkies. Explicit towers of Drinfeld modular curves. 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Ueber algebraische Gebilde mit eindeutigen Transformationen in sich. Math. Ann., 41(3):403–442, 1892. [18] Tomoyoshi Ibukiyama. On rational points of curves of genus 3 over finite fields. Tohoku Math. J. (2), 45(3):311–329, 1993. [19] Yasutaka Ihara. Some remarks on the number of rational points of algebraic curves over finite fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28(3):721–724 (1982), 1981. [20] Kenkiti Iwasawa and Tsuneo Tamagawa. Correction. On the group of auto- morphisms of a function field. J. Math. Soc. Japan, 4:100–101, 1952. [21] E. Kani and M. Rosen. Idempotent relations and factors of Jacobians. Math. Ann., 284(2):307–327, 1989. [22] G. Korchmaros and M. Giulietti. A new family of maximal curves over a finite field, 2007. http://arxiv.org/abs/0711.0445. [23] Kristin Lauter. Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields. J. Algebraic Geom., 10(1):19–36, 2001. With an appendix in French by J.-P. Serre. [24] Kristin Lauter. The maximum or minimum number of rational points on genus three curves over finite fields. Compositio Math., 134(1):87–111, 2002. With an appendix by Jean-Pierre Serre. [25] Yu. I. Manin. What is the maximum number of points on a curve over F2? J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28(3):715–720 (1982), 1981. 62 [26] J. S. Milne. Jacobian varieties. In Arithmetic geometry (Storrs, Conn., 1984), pages 167–212. Springer, New York, 1986. [27] Harald Niederreiter and Chaoping Xing. Rational points on curves over finite fields: theory and applications, volume 285 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2001. [28] Frans Oort and Kenji Ueno. Principally polarized abelian varieties of dimen- sion two or three are Jacobian varieties. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 20:377–381, 1973. [29] Peter Roquette. Absch¨atzung der Automorphismenanzahl von Funktio- nenk¨orpern bei Primzahlcharakteristik. Math. Z., 117:157–163, 1970. [30] Alexander Schiemann. Classification of Hermitian forms with the neighbour method. J. Symbolic Comput., 26(4):487–508, 1998. [31] Hermann Ludwig Schmid. Uber¨ die Automorphismen eines algebraischen Funktionenk¨orpers von Primzahlcharakteristik. J. reine angew. Math., 179:5– 15, 1938. [32] Rainer Schulze-Pillot. Letter to Alexey Zaytsev. 2006. [33] Jean-Pierre Serre. Nombres de points des courbes alg´ebriques sur Fq.In Seminar on number theory, 1982–1983 (Talence, 1982/1983),volumeExp. No. 22, 8. Univ. Bordeaux I, Talence, 1983. [34] Jean-Pierre Serre. Rational points on curves over finite fields. Notes of lectures at Harvard University. 1985. [35] Jean-Pierre Serre. Œuvres. Vol. III. Springer-Verlag, Berlin, 1986. 1972–1984. [36] V. Shabat. Curves with Many Points. Amsterdam, 2001. Ph. D. thesis. [37] Carl Ludwig Siegel. 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