Oliver Lorscheid

activity

20232026

F_{1}

-geometry: bands and band schemes

2 citations · 4 across the 10 of their papers we have counts for

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Showing 2024Show all

2 papers · 1 filter

math.CO2024

The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids

Matthew Baker, Oliver Lorscheid, Zach Walsh +1

We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we sh…

math.AG2024★ 2 cited

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…

The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids

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

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