A family of asymptotically bad wild towers of function fields

TL;DR

This paper investigates a family of wild towers of function fields, providing new conditions under which these towers have infinite genus, expanding understanding of their asymptotic properties in algebraic geometry.

Contribution

It introduces less restrictive conditions for wild towers of function fields to have infinite genus, broadening the class of towers known to exhibit this property.

Findings

Identifies conditions for infinite genus in wild towers

Extends previous results with weaker assumptions

Provides examples of wild towers with infinite genus

Abstract

In a previous work general conditions were given to prove the infiniteness of the genus of certain towers of function fields over a perfect field. It was shown that many examples where particular cases of those general results. In this paper the genus of a family of wild towers of function fields will be considered together with a result with less restrictive sufficient conditions for a wild tower to have infinite genus.