On a theorem of Lafforgue

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.

11 pages. v2: Generalized Theorem 2.3, made some minor expository changes