On a theorem of Lafforgue

TL;DR

This paper provides a new proof and generalizations of a folklore theorem stating that rigid matroids have finitely many projective equivalence classes of representations over any field.

Contribution

It introduces a novel proof technique and extends the theorem to broader classes of matroids.

Findings

Rigid matroids have finitely many representations over any field.

The proof offers new insights into matroid representation theory.

Generalizations expand applicability to more matroid classes.

Abstract

We give a new proof, along with some generalizations, of a folklore theorem (attributed to Laurent Lafforgue) that a rigid matroid (i.e., a matroid with indecomposable basis polytope) has only finitely many projective equivalence classes of representations over any given field.