2023/12/05 by Bhaduri, Anirban, Dey, Souvik, Lank, Pat
#13D09 #14A22 #14A30 #14F08 (primary) #16E35 #16S38 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2312.02840
This work demonstrates classical generation is preserved by the derived pushforward along the structure morphism of a noncommutative coherent algebra to its underlying scheme. Additionally, we establish that the Krull dimension of a variety over a field is a lower bound for the Rouquier dimension of the bounded derived category associated with a noncommutative coherent algebra on it. This is an extension of a classical result of Rouquier to the noncommutative context.