Genus Fields of Congruence Function Fields

Myriam Maldonado-Ramírez, Martha Rzedowski-Calderón, Gabriel Villa-Salvador

Published 2015-12-27Version 1

Let $k$ be a rational congruence function field and consider an arbitrary finite separable extension $K/k$. If for each prime in $k$ ramified in $K$ we have that at least one ramification index is not divided by the characteristic of $K$, we find the genus field $\g K$, except for constants, of the extension $K/k$. In general, we describe the genus field of a global function field.