The Neron model over the Igusa curves

TL;DR

This paper studies the geometry of rational p-division points in degenerating elliptic curves over Igusa curves, classifying reduction types and analyzing wild ramification in characteristics 2 and 3.

Contribution

It provides a classification of Kodaira symbols and reduction types for the universal elliptic curve over Igusa moduli spaces, especially in challenging characteristics.

Findings

Classification of possible Kodaira symbols in degenerating families

Determination of reduction types for the universal curve over Igusa curves

Analysis of wild ramification phenomena in characteristics 2 and 3

Abstract

We analyze the geometry of rational p-division points in degenerating families of elliptic curves in characteristic p. We classify the possible Kodaira symbols and determine for the Igusa moduli problem the reduction type of the universal curve. Special attention is paid to characteristic 2 and 3 where wild ramification and stacky phenomena show up.