2009/02/27 by A. Nyman, Adam Nyman, Nyman, Adam
Mathematics · #18F99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:18F99
paper · pdf · doi:10.48550/arxiv.0902.4886
45 pages. Final version. To appear in J. Pure Appl. Algebra
openalex publication_date 2009/02/27 · arxiv created 2010/01/03 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study obstructions to a direct limit preserving right exact functor F between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. When the domain scheme is affine, or if F is exact, all obstructions vanish and we recover the Eilenberg-Watts Theorem. This result is crucial to the proof that the noncommutative Hirzebruch surfaces constructed by C. Ingalls and D. Patrick are noncommutative ℙ1-bundles in the sense of M. Van den Bergh.