Matthew Baker

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math.AG2026

Elliptic matroids and modular curves

Matthew Baker

For $n \geq 4$ , let $T_{n}$ be the rank-3 matroid on $Z / n Z$ whose bases are the three-element non-zero-sum subsets. Let $X_{1} (n)^{\circ}$ denote the open subscheme of t…

math.AG2025

New building blocks for $F_{1}$ -geometry: bands and band schemes

Matthew Baker, Tong Jin, Oliver Lorscheid

We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sen…

Elliptic matroids and modular curves

New building blocks for F1​-geometry: bands and band schemes

New building blocks for $F_{1}$ -geometry: bands and band schemes