TY - UNPB
T1 - Rigidity, Residues and Duality
T2 - Overview and Recent Progress
AU - Yekutieli, Amnon
N1 - 20 pages
PY - 2021/1/30
Y1 - 2021/1/30
N2 - In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec Duality, the rigid approach concentrates on the construction of rigid residue complexes over rings, and their intricate yet robust properties. The geometrization, i.e. the passage to rigid residue complexes on schemes and Deligne-Mumford (DM) stacks, by gluing, is fairly easy. In the geometric part of the theory, the main results are the Rigid Residue Theorem and the Rigid Duality Theorem for proper maps between schemes, and for tame proper maps between DM stacks.
AB - In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec Duality, the rigid approach concentrates on the construction of rigid residue complexes over rings, and their intricate yet robust properties. The geometrization, i.e. the passage to rigid residue complexes on schemes and Deligne-Mumford (DM) stacks, by gluing, is fairly easy. In the geometric part of the theory, the main results are the Rigid Residue Theorem and the Rigid Duality Theorem for proper maps between schemes, and for tame proper maps between DM stacks.
KW - math.AG
KW - math.AC
KW - math.CT
KW - Primary: 14F08. Secondary: 18G80, 13D09, 14A20, 18F20, 16E45
U2 - 10.48550/arXiv.2102.00255
DO - 10.48550/arXiv.2102.00255
M3 - Preprint
BT - Rigidity, Residues and Duality
ER -