Coherent I-indexed algebras and noncommutative projective schemes

2025/07/18 by Ryder, Jackson
#Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2507.13828

Abstract

We study coherent I-indexed algebras and associated noncommutative projective schemes, where the index set I is a locally finite directed poset. Our main result is a characterisation of such noncommutative projective schemes in terms of sequences of objects with properties analogous to the sequence of tensor powers of an ample line bundle, extending a similar characterisation given by Polishchuk for coherent ℤ-indexed algebras.

Citations

• Compact moduli of marked noncommutative cubic surfaces
• A categorical characterization of quantum projective spaces
• An abstract characterization of noncommutative projective lines
• ℤ²-algebras as noncommutative blow-ups
• Symmetric noncommutative birational transformations
• The geometry of arithmetic noncommutative projective lines
• Abelian and derived deformations in the presence of Z-generating geometric helices
• Noncommutative Proj and coherent algebras
• Generators and representability of functors in commutative and noncommutative geometry

Related

• Coherent algebras and noncommutative projective lines
• Descent and generation for noncommutative coherent algebras over schemes
• Invariants of noncommutative projective schemes
• Noncommutative Proj and coherent algebras
• Locally type FP_n and n-coherent categories