Intersections in Lubin-Tate space and biquadratic fundamental lemmas

TL;DR

This paper computes intersection multiplicities in Lubin-Tate spaces and establishes a new fundamental lemma linking these intersections to derivatives of orbital integrals, advancing understanding in arithmetic geometry.

Contribution

It introduces a novel arithmetic fundamental lemma connecting intersection theory in Lubin-Tate spaces with orbital integral derivatives.

Findings

Explicit formulas for intersection multiplicities.

A new fundamental lemma relating intersections to orbital integral derivatives.

Enhanced understanding of local arithmetic invariants.

Abstract

We compute the intersection multiplicities of special cycles in Lubin-Tate spaces, and formulate a new arithmetic fundamental lemma relating these intersections to derivatives of orbital integrals.