The non-ordinary locus of the TTV family of curves

TL;DR

This paper explores the connection between the non-ordinary locus of the TTV family of curves in characteristic p and the genus of specific triangular modular curves, revealing new insights into their geometric properties.

Contribution

It establishes a novel relation between the non-ordinary locus of TTV curves and the genus of triangular modular curves, advancing understanding of their arithmetic geometry.

Findings

Identifies a link between non-ordinary locus and modular curve genus

Provides formulas relating these geometric invariants

Enhances understanding of reduction properties of TTV curves

Abstract

This article establishes a relation between the non-ordinary locus of the reduction mod $p$ of the TTV family of curves and the genus of certain triangular modular curves.