English

On a theorem of Lafforgue

Combinatorics 2023-09-12 v2 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.2309.01746,
  title  = {On a theorem of Lafforgue},
  author = {Matthew Baker and Oliver Lorscheid},
  journal= {arXiv preprint arXiv:2309.01746},
  year   = {2023}
}

Comments

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

R2 v1 2026-06-28T12:12:27.926Z