2014/11/20 by David Eisenbud, Daniel Erman, Frank-Olaf Schreyer +1 · 23 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Artificial intelligence #Coherent sheaf #Cohomology #Computer science #Functor #Group cohomology #Mathematics #Monad (category theory) #Projective test #Pure mathematics #Resolution (logic) #Sheaf #Sheaf cohomology #math.AG #msc:13D02 #msc:14F05 #msc:14Q99
paper · pdf · doi:10.1007/s40306-015-0126-z
published in Acta Mathematica Vietnamica 40(1), 5-36 (Springer Science+Business Media)
arxiv created 2014/11/20 · openalex publication_date 2015/03/01 · arxiv updated 2018/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe the Tate resolution of a coherent sheaf or complex of coherent sheaves on a product of projective spaces. Such a resolution makes explicit all the cohomology of all twists of the sheaf, including, for example, the multigraded module of twisted global sections, and also the Beilinson monads of all twists. Although the Tate resolution is highly infinite, any finite number of components can be computed efficiently, starting either from a Beilinson monad or from a multigraded module.