Mathematische Zeitschrift

, Volume 259, Issue 3, pp 471–479 | Cite as

The ramification sequence for a fixed point of an automorphism of a curve and the Weierstrass gap sequence



For nonsingular projective curves defined over algebraically closed fields of positive characteristic the dependence of the ramification filtration of decomposition groups of the automorphism group with Weierstrass semigroups attached at wild ramification points is studied. A faithful representation of the p-part of the decomposition group at each wild ramified point to a Riemann–Roch space is defined.


Automorphism Group Faithful Representation Decomposition Group Pole Number Local Uniformizer 


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  1. 1.
    Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: The user language. J. Symbolic Comput. 24 (3–4), 235–265 (1997). Computational algebra and number theory (London, 1993)Google Scholar
  2. 2.
    Cornelissen G. and Kato F. (2003). Equivariant deformation of Mumford curves and of ordinary curves in positive characteristic. Duke Math. J. 116(3): 431–470 CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Elkies, N.D.: Linearized algebra and finite groups of Lie type. I. Linear and symplectic groups, Applications of curves over finite fields (Seattle, WA, 1997), Contemp. Math., vol 245, pp 77–107. Amer. Math. Soc., Providence (1999)Google Scholar
  4. 4.
    Goldschmidt D.M. (2003). Algebraic functions and projective curves, Graduate Texts in Mathematics, vol. 215. Springer, New York Google Scholar
  5. 5.
    Goss D. (1996). Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol 35. Springer, Berlin Google Scholar
  6. 6.
    Köck B. (2004). Galois structure of Zariski cohomology for weakly ramified covers of curves. Am. J. Math. 126(5): 1085–1107 CrossRefMATHGoogle Scholar
  7. 7.
    Kontogeorgis A.I. (1998). The group of automorphisms of the function fields of the curve x n + y m + 1 = 0. J. Number Theory 72(1): 110–136 CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Lehr C. and Matignon M. (2005). Automorphism groups for p-cyclic covers of the affine line. Compos. Math. 141(5): 1213–1237 CrossRefMathSciNetMATHGoogle Scholar
  9. 9.
    Leopoldt H.-W. (1996). Uber die Automorphismengruppe des Fermatkörpers. J. Number Theory 56(2): 256–282 CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Nakajima S. (1987). p-ranks and automorphism groups of algebraic curves. Trans. Am. Math. Soc. 303(2): 595–607 CrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    Roquette P. (1970). Abschätzung der Automorphismenanzahl von Funktionenkörpern bei Primzahlcharakteristik. Math. Z. 117: 157–163 CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    Serre, J.-P.: Local fields. Springer, New York (1979). Translated from the French by Marvin Jay GreenbergGoogle Scholar
  13. 13.
    Stichtenoth H. (1973). Über die Automorphismengruppe eines algebraischen Funktionenkörpers von Primzahlcharakteristik. II. Ein spezieller Typ von Funktionenkörpern. Arch. Math. (Basel) 24: 615–631 MathSciNetMATHGoogle Scholar
  14. 14.
    Stichtenoth H. (1993). Algebraic Function Fields and Codes. Springer, Berlin MATHGoogle Scholar
  15. 15.
    Geer G. and Vlugt M. (1992). Reed–Muller codes and supersingular curves. I. Compos. Math. 84(3): 333–367 MATHGoogle Scholar

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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the ÆgeanKarlovassiGreece

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