IJPAM: Volume 38, No. 4 (2007)

ON ELEMENTARY ABELIAN $p$-EXTENSIONS
WITH NULL HASSE-WITT MAP

Myriam R. Maldonado-Ramírez$^{1,2}$, Martha Rzedowski-Calderón$^2$
$^1$Departamento de Matemáticas
Escuela Superior de Física y Matemáticas
Instituto Politécnico Nacional
Unidad Profesional Adolfo López Mateos
México, D.F., C.P. 07300 MÉXICO
e-mail: mmaldonado@ctrl.cinvestav.mx
$^2$Departamento de Control Automático
Centro de Investigación y de Estudios Avanzados del I.P.N.
Apartado Postal 14-740, México, D.F., 07000, MÉXICO
e-mail: mrzedowski@ctrl.cinvestav.mx


Abstract.The Hasse-Witt map provides arithmetic information about function field extensions of characteristic $p$. In this paper we study several kinds of $p$-extensions of a rational function field over an algebraically closed field of characteristic $p$, with emphasis on elementary Abelian $p$-extensions and prove that their Hasse-Witt map is almost always non null.

Received: June 13, 2007

AMS Subject Classification: 11R58, 14H05

Key Words and Phrases: Hasse-Witt map, Hasse-Witt matrix, Holomorphic differentials

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 38
Issue: 4