The p-rank of the reduction \rmmod p of jacobians and Jacobi sums

2011/11/02 by A. Álvarez, Álvarez, A.
Mathematics · Computer Science · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1111.0545

Abstract

Let Y_K→ X_K be a ramified cyclic covering of curves, where K is a cyclotomic field. In this work we study the p-rank of the reduction \rmmod p of a model of the jacobian of Y_K. In this way, we obtain counterparts of the Deuring polynomial, defined for elliptic curves, for genus greater than one. Moreover, we show that curves Y_K give Hecke characters for cyclotomic fields. To carry out this study we use Jacobi sums and certain L-functions.

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