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Galois module structure of holomorphic differentials

  • Martha Rzedowski-Calderón (a1), Gabriel Villa-Salvador (a1) and Manohar L. Madan (a2)

Abstract

For a finite cyclic P–extension L/K of a rational function field K = κ(x) over an algebraically closed field κ of characteristic P > 0 such that every ramified prime divisor is fully ramified, we find a basis of the κ[G]-module structure of ωL(0) in terms of indecomposable modules.

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References

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[1]Boseck, H., ‘Zur Theorie der Weierstraζpunkte’, Math. Nachr. 19 (1958), 2963.
[2]Chevalley, C. and Weil, A., ‘Über das Verhalten der Integrale 1. Gattung bei Automorphismen des Funktionenkörpers’, Abh. Math. Sem. Univ. Hamburg 10 (1934), 358361.
[3]Garcia, A., ‘On Weierstrass points on certain elementary Abelian P–extensions of algebraic function fieldsManuscripta Math. 72 (1991), 6779.
[4]Madden, D., ‘Arithmetic of generalized Artin-Schreier extensions of κ(x)’, J. Number Theory 10 (1978), 303323.
[5]Rzedowski-Calderón, M., Villa-Salvador, G. and Madan, M., ‘Galois module structure of holomorphic differentials in characteristic P’, Arch. Math. 66 (1996), 150156.
[6]Schmid, H.L., ‘Zur Arithmetik der zyklischen P–Körper’, J. Reine Angew. Math. 176 (19361937), 161167.
[7]Serre, J.-P., Local fields, Graduate Texts in Mathematics 67 (Springer-Verlag, Berlin, Heidelberg, New York, 1979).
[8]Valentini, R. and Madan, M., ‘Automorphisms and holomorphic differentials in characteristic P’, J. Number Theory 13 (1981), 106115.
[9]Witt, E., ‘Zyklishe Körper und Algebren der Characteristik P vom Grad P n’, J. Reine Angew. Math. 176 (19361937), 126140.
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Galois module structure of holomorphic differentials

  • Martha Rzedowski-Calderón (a1), Gabriel Villa-Salvador (a1) and Manohar L. Madan (a2)

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