Explicit Riemann-Roch spaces in the Hilbert class field

2023/09/13 by Couveignes, Jean-Marc, Gasnier, Jean · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.06754

Abstract

Let \mathbf K be a finite field, X and Y two curves over \mathbf K, and Y→ X an unramified abelian cover with Galois group G. Let D be a divisor on X and E its pullback on Y. Under mild conditions the linear space associated with E is a free \mathbf K[G]-module. We study the algorithmic aspects and applications of these modules.

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