Preview
Unable to display preview. Download preview PDF.
Bibliography
Algebra, Mathematical Logic, Number Theory, Topology (survey articles on the occasion of the fiftieth anniversary of the Steklov Mathematical Institute of the USSR Academy of Sciences). Proc. Steklov Inst. Math., 1984, 168.
Algebraic Surfaces. Proc. Steklov Inst. Math., 1965, 75, 281 pp.
S. Yu. Arakelov. Intersection theory of divisors on an arithmetic surface. Math. USSR, Izv., 1974, 8, 1167–1180.
S. Yu. Arakelov. Theory of intersections on an arithmetic surface. In: Proceedings of the International Congress of Mathematicians (Vancouver, 1974), V. 1. Montreal: Canad. Math. Congress, 1975, 405–408.
Z. I. Borevich, I. R. Shafarevich. Number Theory (transl. N. Greenleaf). New York-London: Academic Press, 1966 (Pure Appl. Math., 20).
J. B. Bost. Fibrés déterminants, déterminants régularisés et mesures sur les espaces de modules des courbes complexes. In: Séminaire Bourbaki, février 1987, exposé 676. Astérisque, 152–153. Paris: Soc. Math. France, 1987, 113–149.
H. Brückner. Eine explizite Formel zum Reziprozitätsgesetz für Primzahlexponenten p. In: Algebraische Zahlentheorie (Oberwolfach, 1964). Mannheim: Bibliographisches Institut, 1967, 31–39.
H. Brückner. Explizites Reziprozitätsgesetz und Anwendungen. Vorles. Fachber. Math. Univ. Essen, 1979, Heft 2.
H. Cartan. Séminaire École Normale Supérieure, 1950/51, 1951/52, 1953/54, 1957/58. Secrétariat mathématiques, Paris.
J. W. S. Cassels, A. Frölich. Algebraic Number Theory. London: Academic Press, 1967.
N. G. Chebotarev. Theory of Algebraic Functions. Moscow-Leningrad: Gostekhizdat, 1948 (Russian).
P. Deligne. Intersections sur les surfaces régulières. In: Groupes de monodromie en géométrie algébrique. II (SGA 7 II, 1967–1969). Berlin-New York: Springer, 1973, exposé X, 1–38 (Lecture Notes in Math., 340).
P. Deligne. Le déterminant de la cohomologie. In: Current Trends in Arithmetical Algebraic Geometry (Arcata, CA, 1985). Providence, RI: Amer. Math. Soc., 1987, 93–177 (Contemp. Math, 67).
P. Deligne. Quelques idées maîtresses de l’œuvre de A. Grothendieck. Matériaux pour l’histoire des matématiques au XXième siècle. Actes de colloque à la mémoire de Jean Dieudonné (Nice, 1996). Paris: Soc. Math. France, 1998, 11–20 (Séminaires et Congrès, 3).
S. P. Demushkin et al. Igor’ Rostislavovich Shafarevich (on his sixtieth birthday). Russ. Math. Surveys, 1984, 39(1), 189–200.
F. Enriques. Le superficie algebriche. Bologna: Nicola Zanichelli, 1949.
D. K. Faddeev. On Hilbert’s ninth problem. In: The Hilbert Problems. Moscow: Nauka, 1969, 131–140 (Russian).
G. Faltings. Calculus on arithmetic surfaces. Ann. Math., 1984, 119, 387–424.
G. Faltings. Lectures on the Arithmetic Riemann-Roch Theorem. Princeton, NJ, 1992 (Ann. Math. Studies, 127).
A. Grothendieck. The cohomology theory of abstract algebraic varieties. In: Proceedings of the International Congress of Mathematicians (Edinburgh, 1958). Cambridge University Press, 1960, 103–118.
K. Hensel. Theorie der algebraischen Zahlen. Leipzig: B. G. Teubner, 1908.
D. Hilbert. Über die Theorie der relativquadratischer Zahlkörper. Jahresber. Deutsch. Math.-Verein., 1899, 6; Gesammelte Abhandlungen [23], Bd. 1, 364–369.
D. Hilbert. Gesammelte Abhandlungen, Bd. 1–3. Berlin: Springer, 1932–1935; New York: Chelsea, 1965 (reprint); Russian translation: D.Hilbert. Selected Works, V. 1–2. Moscow: Factorial, 1998.
D. Hilbert. Mathematische Probleme. In: Gesammelte Abhandlungen [23], Bd. 2, 401–436.
W. V. D. Hodge. The Theory and Applications of Harmonic Integrals. Cambridge University Press, 1941.
A. I. Kostrikin et al. Vasilii Alekseevich Iskovskikh (on his 60th birthday). Russ. Math. Surveys, 1999, 54(4), 863–868.
S. Lang. Fundamentals of Diophantine Geometry. New York: Springer, 1983.
S. Lang. Introduction to Arakelov Theory. New York: Springer, 1988.
A. I. Lapin. The theory of the Shafarevich symbol. Izv. Akad. Nauk SSSR, Ser. Mat., 1953, 17, 31–50 (Russian).
A. I. Lapin. On the theory of the Shafarevich symbol. Izv. Akad. Nauk SSSR, Ser. Mat., 1954, 18, 145–158 (Russian).
A. I. Lapin. The general reciprocity law and a new foundation of class-field theory. Izv. Akad. Nauk SSSR, Ser. Mat., 1954, 18, 335–378 (Russian).
S. Lichtenbaum. Curves over discrete valuation rings. Amer. J. Math., 1968, 15, 380–405.
A. Néron. Quasi-fonctions et hauteurs sur les variétés abéliennes. Ann. Math., 1965, 82, 249–331.
I. Newton. The Mathematical Works, Vol. I, II. Assembled with an introduction by D. T. Whiteside. New York-London: Johnson Reprint Corp., 1964; 1967.
O. A. Oleinik. On Hilbert’s sixteenth problem. In: The Hilbert Problems. Moscow: Nauka, 1969, 182–195.
A. N. Parshin. Modular correspondences, heights, and isogeny of Abelian varieties. Trudy Matem. Inst. im. Steklova, 1973, 132, 211–236 (Russian).
A. N. Parshin. On the application of ramified coverings in the theory of Diophantine equations. Math. USSR, Sb., 1990, 66(1), 249–264.
Proceedings of the International Congress of Mathematicians (Cambridge, MA, 1950), V. 1. Providence, RI: Amer. Math. Soc., 1952, p. 122.
J.-P. Serre. Faisceaux algébriques cohérents. Ann. Math., 1955, 61, 197–278.
I. R. Shafarevich. The general reciprocity law. Matem. Sb., 1950, 26, 113–146 (Russian).
I. R. Shafarevich. Algebraic number fields. In: Proceedings of the International Congress of Mathematicians (Stockholm, 1962). Djursholm: Institut Mittag-Leffler, 1963, 163–176 (Russian).
I. R. Shafarevich. Lectures on Minimal Models and Birational Transformations of Two-Dimensional Schemes. Bombay: Tata Institute of Fundamental Research, 1966.
C. L. Siegel. Analytic Functions of Several Complex Variables. Lectures delivered at the Institute for Advanced Study, 1948–1949.
C. L. Siegel. Automorphic Functions of Several Complex Variables. Moscow: Inostrannaya Literatura, 1954 (Russian translation).
C. Soulé (with D. Abramovich, J.-F. Burnol, and J. Kramer). Lectures on Arakelov Geometry. Cambridge University Press, 1992.
C. Soulé. Hermitian vector bundles on arithmetic varieties. Proc. Symp. Pure Math., 1997, 62, Part 1, 383–419.
C. Soulé. On the field with one element. Talk given at the Arbeitstagung, Bonn, June 1999. Preprint IHES/M/99/55.
C. Soulé, S. Bloch, H. Gillet. Non-Archimedean Arakelov theory. J. Alg. Geom., 1995, 4, 427–485.
L. Szpiro, ed. Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell. Astérisque, 127. Paris: Soc. Math. France, 1985.
V. S. Vladimirov, I. V. Volovich, E. I. Zelenov. p-Adic Analysis and Mathematical Physics. River Edge, NJ: World Scientific, 1994.
S. V. Vostokov. Explicit form of the law of reciprocity. Math. USSR, Izv., 1978, 13, 557–588.
A. Weil. Number-theory and algebraic geometry. In: Proceedings of the International Congress of Mathematicians (Cambridge, MA, 1950), Vol. 2. Providence, RI: Amer. Math. Soc., 1952, 90–110; André Weil. Œuvres Scientifiques/Collected Papers, Vol. 1 (1926–1951). Heidelberg-Berlin: Springer, 1980 (corrected second printing), 442–452.
A. Weil. Introduction à l’étude des variétés kählériennes. Paris: Hermann, 1958.
Yu. G. Zarkhin, A. N. Parshin. Finiteness problems in Diophantine geometry. Appendix to the Russian translation of: S. Lang. Fundamentals of Diophantine Geometry. Moscow: Mir, 1986, 369–448 (Russian).
S. Zdravkovska, P. Duren, eds. The Golden Years of Moscow Mathematics. Providence, RI: Amer. Math. Soc., 1993.
S. Zhang. Admissible pairing on a curve. Invent. Math., 1993, 112(1), 171–193.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Parshin, A.N. (2006). Numbers as Functions: The Development of an Idea in the Moscow School of Algebraic Geometry. In: Bolibruch, †.A.A., et al. Mathematical Events of the Twentieth Century. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-29462-7_15
Download citation
DOI: https://doi.org/10.1007/3-540-29462-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23235-3
Online ISBN: 978-3-540-29462-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)