Local heights on elliptic curves and intersection multiplicities

TL;DR

This paper establishes a formula connecting local heights on elliptic curves over number fields with intersection theory on regular models, providing a new perspective on height calculations in arithmetic geometry.

Contribution

It introduces a novel formula linking local heights to intersection theory on regular models of elliptic curves over number fields.

Findings

Derived a formula for local heights using intersection theory.

Bridged concepts between height functions and intersection multiplicities.

Enhanced understanding of arithmetic properties of elliptic curves.

Abstract

In this short note we prove a formula for local heights on elliptic curves over number fields in terms of intersection theory on a regular model over the ring of integers.