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math.AG2024★ 2 cited
New building blocks for -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…
math.AG2023★ 1 cited
The topological shadow of F1-geometry: congruence spaces
Oliver Lorscheid, Samarpita Ray
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This lead…