DOI QR코드

DOI QR Code

THE DIVISOR CLASS GROUP OF SURFACES OVER FINITE FIELDS

  • Choi, Sang-Ki (Department of Mathematics Education, Konkuk University)
  • Received : 2011.05.11
  • Accepted : 2011.07.18
  • Published : 2011.08.31

Abstract

We investigate the divisor class group of surfaces over finite fields. For some surfaces the divisor class group depends on the characteristic of the field. We calculate the determinant of a matrix which will provide an information about the divisor class group of the surfaces.

Acknowledgement

Supported by : Konkuk University

References

  1. M. Auslander & D. Buchsbaum: Homological dimensions in local rings. Trans. Amer. Math. Soc. 85 (1957), 390-405. https://doi.org/10.1090/S0002-9947-1957-0086822-7
  2. D. Buchsbaum: Some remarks on factorization in power series rings. J. Math. Mech. 10 (1961), 749-753.
  3. S. Choi: The divisor class group of surfaces of embedding dimension 3. J. Algebra 119 (1988), 162-169. https://doi.org/10.1016/0021-8693(88)90081-6
  4. S. Choi: Unique factorization in two-dimensional complete intersectios. J. Korean Math. Soc. 34 (1997), no. 3, 533-541.
  5. D. Eisenbud: Recent progress in commutative algebra. Algebraic Geometry - Arcata 1974, AMS Proc. of Pure Math. XXIX (1975), 111-128.
  6. R. Fossum: The divisor class group of a Krull domains. Springer Ergebnisse 74, 1973.
  7. J. Lipman: Rational singularities with applications to algebraic surfaces and unique factorizations. IHES 36 (1969), 195-279. https://doi.org/10.1007/BF02684604
  8. J. Lipman: Unique factorization in complete local rings. Algebraic Geometry - Arcata 1974, AMS Proc. of Pure Math. XXIX (1975), 531-546.
  9. D. Mumford: The topology of normal singularities of algebraic surfaces. IHES 9 (1961), 1-22.
  10. P. Salmon: Su un problema posto da P. Samuel. Atti. accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) B 40 (1966), 801-803.
  11. P. Samuel: On unique factorization domains. Illinois J. Math. 5 (1961), 1-17.
  12. P. Samuel: Sur les anneaux factoriels Bull. Soc. Math. France 89 (1961), 155-173.
  13. G. Scheja: Einiege Beispiele faktorieller lokaler Ringe. Math. Annelen 152 (1967), 124-134.
  14. N. Zinn-Justine: Deviations dans les corpset anneaux de characteristique p. Bull. Soc. Math. France, Suppl., Mem. 10 (1967), 10.
  15. N. Zinn-Justine: Descentep-radicelle et factorialite. Colloque d'algebre, 6-7 mai 1967, Paris : Secrtariat mathematique, 1968.