Rocky Mountain Journal of Mathematics

Genus formulas for abelian $p$-extensions

Fausto Jarquin-Zarate, Martha Rzedowski-Calderon, and Gabriel Villa-Salvador

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We apply a result of Kani relating genera and Hasse-Witt invariants of Galois extensions to a family of abelian $p$-extensions. Our formulas generalize the case of elementary abelian $p$-extensions found by Garcia and Stichtenoth.

Article information

Rocky Mountain J. Math., Volume 48, Number 6 (2018), 1905-1915.

First available in Project Euclid: 24 November 2018

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Zentralblatt MATH identifier

Primary: 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]
Secondary: 111R29 11R60: Cyclotomic function fields (class groups, Bernoulli objects, etc.)

Function fields Kani's formula abelian $p$-extensions Artin-Schreier-Witt extensions


Jarquin-Zarate, Fausto; Rzedowski-Calderon, Martha; Villa-Salvador, Gabriel. Genus formulas for abelian $p$-extensions. Rocky Mountain J. Math. 48 (2018), no. 6, 1905--1915. doi:10.1216/RMJ-2018-48-6-1905.

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  • Arnaldo Garcia and Henning Stichtenoth, Elementary abelian $p$-extensions of algebraic function fields, Manuscr. Math. 72 (1991), 67–79.
  • Ernst Kani, Relations between the genera and between the Hasse-Witt invariants of Galois coverings of curves, Canadian Math. Bull. 28 (1985), 321–327.
  • Hermann Ludwig Schmid, Zur Arithmetik der zyklischen $p$-Körper, J. reine angew. Math. 176 (1936), 161–167.