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The ring of algebraic correspondences on a generic curve of genus g

Published online by Cambridge University Press:  22 January 2016

Yoshiaki Ikeda*
Affiliation:
Tokyo University of Education
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0. Let p be a prime number or zero and let g be a non-negative integer. Then there is a coarse moduli space Mg for complete non-singular irreducible curves of genus g defined over fields of characteristic p, which is an irreducible variety over the algebraic closure p of the prime field Fp. (Especially, F0 is also denoted by Q as usual.) ([8], [2]). The curve corresponding to a generic point of Mg over p is called a generic curve of genus g.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Baily, W. L. Jr. : On the automorphism group of a generic curve of genus g>2, J. Math. Kyoto, 1 (1961), 101108; Correction, 325.Google Scholar
[2] Deligne, P. and Mumford, D. : The irreducibility of the space of curves of given genus, Publ. Math. I.H.E.S., No. 36 (Volume dedicated to Zariski, O.), 1969, 75109.Google Scholar
[3] Deuring, M. : Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14 (1941), 197272.CrossRefGoogle Scholar
[4] Deuring, M. : Invarianten und Normaliormen elliptischer Funktionenkörper, Math. Zeitschr., 47 (1941), 4756.Google Scholar
[5] Grothendieck, A.: Séminaire de géométrie algébrique, 1960/61, Exporé III.Google Scholar
[6] Koizumi, S. : The fields of moduli for polarized abelian varieties and for curves, Nagoya Math. J., 48 (1972), 3755.Google Scholar
[7] Koizumi, S. and Shimura, G. : On specializations of abelian varieties, Scientific Papers of College of General Education, Univ. of Tokyo, 9 (1959), 187211.Google Scholar
[8] Mumford, D. : Geometric invariant theory, Erg. d. Math., Neue F. Bd. 34, Springer Verlag, 1965.Google Scholar
[9] Mumford, D. : Bi-extensions of formal groups, Algebraic geometry, Tata Inst. Fund. Research, Bombay, Oxford Univ. Press, 1969, 307322.Google Scholar
[10] Mumford, D.: Abelian varieties, Tata Inst. Studies in Math., 5, Oxford Univ. Press, 1970.Google Scholar
[11] Oort, F.: Finite group schemes, local moduli for abelian varieties, and lifting problems, Comp. Math., 23 (1971), 265296 (also: Algebraic Geometry, Oslo, 1970, Wolters-Noordhoff, 1972.)Google Scholar
[12] Oort, F. and Ueno, K.: Principally polarized abelian varieties of dimension two or three are Jacobian varieties, Jour. Fac. of Sci., Univ. of Tokyo, Sec. IA, 20 (1973), 377381.Google Scholar
[13] Schlessinger, M.: Functors of artin rings, Transact. Amer. Math. Soc., 130 (1968), 208222.Google Scholar
[14] Shimura, G. and Taniyama, Y.: Complex multiplication of abelian varieties and its applications to number theory, Publ. of Math. Soc. of Japan, 1961.Google Scholar
[15] Weil, A.: Zum Beweis des Torellischen Satzes, Akad. Wiss. Göttingen, math.-phys. Klasse, 1957, No. 2, 3353.Google Scholar
[16] Weil, A.: Foundations of algebraic geometry, Amer. Math. Society, Providence, R. I., 1946, 2nd edition, 1962.Google Scholar