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On the galois module structure of semisimple holomorphic differentials

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Abstract

LetL/K be a finite Galoisp-extension of algebraic function fields of one variable over an algebraically closed fieldk of characteristicp, with Galois groupG=Gal(L/K). The space Ώ s L (0) of semisimple holomorphic differentials ofL is thek-vector space of holomorphic differentials which are fixed by the Cartier operator. We obtain the isomorphism classes and multiplicities of the summands in a Krull-Schmidt decomposition of thek[G]-module Ώ s L (0) into a direct sum of indecomposablek[G]-modules.

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Authors and Affiliations

  1. Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo No. 180. Col. Reynosa Tamaulipas Azcapotzalco D.F., C.P. 02200, Mexico, D.F.

    Pedro Ricardo López-Bautista

  2. Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del I.P.N., Apartado Postal 14-740, 07000, México, D.F.

    Gabriel Daniel Villa-Salvador

Authors
  1. Pedro Ricardo López-Bautista
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  2. Gabriel Daniel Villa-Salvador
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Correspondence to Pedro Ricardo López-Bautista.

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Partially supported by CONACyT, project No. 25063-E.

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López-Bautista, P.R., Villa-Salvador, G.D. On the galois module structure of semisimple holomorphic differentials. Isr. J. Math. 116, 345–365 (2000). https://doi.org/10.1007/BF02773225

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  • DOI: https://doi.org/10.1007/BF02773225

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