@article{CM_1975__31_2_119_0, author = {Koblitz, Neal}, title = {$p$-adic variation of the zeta-function over families of varieties defined over finite fields}, journal = {Compositio Mathematica}, pages = {119--218}, publisher = {Noordhoff International Publishing}, volume = {31}, number = {2}, year = {1975}, mrnumber = {414557}, zbl = {0332.14008}, language = {en}, url = {http://www.numdam.org/item/CM_1975__31_2_119_0/} }
TY - JOUR AU - Koblitz, Neal TI - $p$-adic variation of the zeta-function over families of varieties defined over finite fields JO - Compositio Mathematica PY - 1975 SP - 119 EP - 218 VL - 31 IS - 2 PB - Noordhoff International Publishing UR - http://www.numdam.org/item/CM_1975__31_2_119_0/ LA - en ID - CM_1975__31_2_119_0 ER -
%0 Journal Article %A Koblitz, Neal %T $p$-adic variation of the zeta-function over families of varieties defined over finite fields %J Compositio Mathematica %D 1975 %P 119-218 %V 31 %N 2 %I Noordhoff International Publishing %U http://www.numdam.org/item/CM_1975__31_2_119_0/ %G en %F CM_1975__31_2_119_0
Koblitz, Neal. $p$-adic variation of the zeta-function over families of varieties defined over finite fields. Compositio Mathematica, Tome 31 (1975) no. 2, pp. 119-218. http://www.numdam.org/item/CM_1975__31_2_119_0/
[1] Supersingular K3 Surfaces (to appear). | Numdam | MR | Zbl
:[2] Zeroes of Polynomials over Finite Fields. Amer. J. Math., 86, 1964. | MR | Zbl
:[3] Algèbre commutative. Paris: Hermann, 1961.
:[4] Une nouvelle opération sur les formes différentielles. C. R. Acad. Sci. Paris 244, 1957. | MR | Zbl
:[5] Théorème de Lefschetz et critères de dégénérescence de suites spectrales. Publ. Math. I.H.E.S. 35, 1969. | EuDML | Numdam | MR | Zbl
:[6] The Irreducibility of the Space of Curves of Given Genus. Publ. Math. I.H.E.S. 36, 1969. | EuDML | Numdam | MR | Zbl
and :[7] Lectures on p-Divisible Groups, Lecture Notes in Mathematics 302, Berlin- Heidelberg-New York: Springer, 1972. | MR | Zbl
:[8] On the Congruence Properties of the Zeta Function of Algebraic Varieties. J. für die Reine und Angewandte Math. 203, 1960. | EuDML | MR | Zbl
:[9] Normalized Period Matrices I and II. Annals of Math. 94, 2nd series, 1971, and Annals of Math. 98, 2nd series, 1973. | Zbl
:[10] On the Rationality of the Zeta Function of an Algebraic Variety. Amer. J. Math. 82, 1960. | MR | Zbl
:[11] On the Zeta Function of a Hypersurface II. Annals of Math. 80, 2nd series, 1964. | MR | Zbl
:[12] Fondements de la géométrie algébrique, Secrétariat Mathématique, 11 rue Pierre Curie, Paris 5e, France, 1962. | MR | Zbl
:[13] Séminaire de géométrie algébrique, 1, Lecture Notes in Mathematics 224, Berlin-Heidelberg-New York: Springer, 1971. | MR | Zbl
:[14] Séminaire de géométrie algébrique, 2, I.H.E.S., 1962. | Zbl
:[15] Existenz Separabler Zyklischer Unverzweigter Erweiterungskörper vom Primzahlgrade p über Elliptischen Funktionenkörpern der Charakteristik p. J. Reine Angew. Math. 172, 1934. | JFM | Zbl
:[16] Zyklische Unverzweigte Erweiterungskörper vom Primzahlgrade p über einem Algebraischen Funktionenkörper der Charakteristik p. Monatsh. für Math. u. Phys. 43, 1936. | JFM | Zbl
and :[17] Isogeny Classes of Abelian Varieties over Finite Fields. J. Math. Soc. Japan 20, 1968. | MR | Zbl
:[18] Arithmetic Variety of Moduli for Genus Two. Annals of Math. 72, 2nd series, 1960. | MR | Zbl
:[19] Class Number of a Definite Quaternion with Prime Discriminant. Proc. Natl. Acad. Sci. 44, 1958. | MR | Zbl
:[20] Algebraic Solutions of Differential Equations (p-Curvature and the Hodge Filtration), Inventiones Math. 18, 1972. | MR | Zbl
:[21] Une formule de congruence pour la fonction ζ. S.G.A. 7 II, Lecture Notes in Mathematics 340, Berlin-Heidelberg-New York: Springer, 1973. | Zbl
:[22] Nilpotent Connections and the Monodromy Theorem: Applications of a Result of Turrittin. Publ. Math. I.H.E.S. 39, 1971. | Numdam | MR | Zbl
:[23] Le niveau de la cohomologie des intersections complètes, S.G.A. 7 II, Lecture Notes in Mathematics 340, Berlin-Heidelberg-New York: Springer, 1973. | Zbl
:[24] A Note on a Theorem of Ax. Amer. J. Math., 93, 1971. | MR | Zbl
:[25] Pinceaux de Lefschetz: théorème d'existence. S.G.A. 7 II, Lecture Notes in Mathematics 340, Berlin-Heidelberg-New York: Springer, 1973. | Zbl
:[26] Review of Gauss Sums à la Stickelberger (unpublished notes).
:[27] Travaux de Dwork. Exp. 409. Séminaire Bourbaki 1971/72, Lecture Notes in Mathematics 317, Berlin-Heidelberg-New York: Springer, 1973. | Numdam | MR | Zbl
:[28] On the Differentiation of De Rham Cohomology Classes with Respect to Parameters. J. Math. Kyoto Univ. 8, 1968. | MR | Zbl
and :[29] Weil Cohomologies in Dix exposés sur la théorie des schémas. Amsterdam: North-Holland, 1969.
:[30] Algebra. Reading, Mass.:Addison-Wesley, 1965. | MR | Zbl
:[31] Algebraic Curves over Fields with Differentiation. A.M.S. Translations (2) 37, 1964. | Zbl
:[32] The Hasse-Witt Matrix of an Algebraic Curve. A.M.S. Translations (2) 45, 1965. | Zbl
:[33] Lekcii po Algebraičeskoĭ Geometrii. Moscow: Izd. Mosk. Univ., 1970.
:[34] The Theory of Commutative Formal Groups over Fields of Finite Characteristic. Translated in Russian Math. Surv. 18, 1963. | MR | Zbl
:[35] Frobenius and the Hodge Filtration. Bull. A.M.S. 78, 1972. | MR | Zbl
:[36] Frobenius and the Hodge Filtration (Estimates), Annals of Math. 98, 2nd series, 1973. | MR | Zbl
:[37] Universal Extensions and One Dimensional Crystalline Cohomology. Lecture Notes in Mathematics 370, Berlin-Heidelberg-New York: Springer, 1974. | MR | Zbl
and :[38] The Crystals Associated to Barsotti-Tate Groups : With Applications to Abelian Schemes. Lecture Notes in Mathematics 264, Berlin-Heidelberg -New York: Springer, 1972. | MR | Zbl
:[39] Curves over a Finite Field with Invertible Hasse-Witt Matrix. Math. Annalen 197, 1972. | Zbl
:[40] Über Gewöhnliche Projektive Hyperflächen (preprint).
:[41] P-adic Analysis and Zeta Functions. Lectures in Mathematics No. 4, Tokyo: Kinokuniya Book-Store Ltd., 1970. | MR | Zbl
:[42] Abelian Varieties. Bombay: Oxford University Press, 1970. | MR | Zbl
:[43] Geometric Invariant Theory. New York: Academic Press, 1965. | MR
:[44] Introduction to Algebraic Geometry (preliminary version of first three chapters). Harvard University.
:[45] Prym Varieties (to appear).
:[46] Introduction to the Theory of Moduli, in Proc. 5th Nordic Summer Sch. The Netherlands: Wolters-Noordhoff Pub., 1970. | MR | Zbl
and :[47] The First De Rham Cohomology Group and Dieudonné Modules. Annales sci. de l'École Norm. Sup., 4e serie 2, 1969. | Numdam | MR | Zbl
:[48] Nakayama's Lemma for Half-Exact Functors. Proc. of the A.M.S. 31, 1972. | MR | Zbl
and :[49] Finite Group Schemes, Local Moduli for Abelian Varieties, and Lifting Problems, in Proc. 5th Nordic Summer Sch. The Netherlands: Wolters-Noordhoff Pub., 1970. | Zbl
:[50] Subvarieties of Moduli Spaces. Inventiones math. 24, 1974. | MR | Zbl
:[51] Foundations of Algebraic Geometry. translated in Russian Math. Surv. 24, 1969. | MR | Zbl
:[52] Functors of Artin Rings. Trans. A.M.S. 130, 1968. | MR | Zbl
:[53] Algèbre Locale. Multiplicités. Lecture Notes in Mathematics 11, Berlin- Heidelberg-New York: Springer, 1965. | MR | Zbl
:[54] Faisceaux algébriques cohérents. Annals of Math. 61, 2nd series, 1955. | MR | Zbl
:[55] Sur la topologie des variétés algébriques en caractéristique p. Symposio Intern. de Top. Alg., Mexico, 1958. | MR | Zbl
:[56] Über eine Verallgemeinerung der Kreistheilung. Math. Ann. 37, 1890. | JFM | MR
:[57] Algebraic Cycles and Poles of Zeta Functions, in Arithmetical Algebraic Geometry (Proc. of Purdue Conf.), New York: Harper and Row, 1965. | MR | Zbl
:[58] Classes d'isogénie des variétés abéliennes sur un corpsfini (d'après T. Honda). Exp. 352, Séminaire Bourbaki 1968/69, Lecture Notes in Mathematics 179, Berlin- Heidelberg-New York: Springer, 1971. | Numdam | Zbl
:[59] Endomorphisms of Abelian Varieties over Finite Fields. Inventiones Math. 2, 1966. | MR | Zbl
:[60] Bemerkung zur Verstehenden Arbeit von Herr Chevalley, Abh. Math. Sem. Univ. Hamburg, 11, 1936. | JFM | Zbl
:[61] Jacobi Sums as 'Grössencharaktere', Trans. A.M.S. 73, 1952. | MR | Zbl
:[62] Numbers of Solutions of Equations in Finite Fields. Bull. A.M.S. 55, 1949. | MR | Zbl
:[63] Les schémas de modules de courbes elliptiques, in Lecture Notes in Mathematics 349 (Proc. Intern. Summer Sch. on Modular Functions), Berlin -Heidelberg-New York: Springer, 1973. | MR | Zbl
and :[64] Simple Abelian Varieties Having a Prescribed Formal Isogeny Type. Univ. of Amsterdam Math. Inst. Report 73-02, 1973.
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