Non-commutative algebraic geometry. An introduction

DOI10.1007/BFB0091730zbMath0477.16001OpenAlexW2479574937MaRDI QIDQ1160168

Freddy M. J. van Oystaeyen, Alain Verschoren

Publication date: 1981

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bfb0091730

zbMATH Keywords

orderscurveslocal ringsgraded ringssheavesRiemann-Roch theoremalgebraic varietyprojective varietiesPI-ringssimple Artinian ringstalkslocalisation in module categoriesPresheavesprime spectrum of noncommutative ringproduct varietiesring of local sections

Mathematics Subject Classification ID

Riemann-Roch theorems (14C40) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Graded rings and modules (associative rings and algebras) (16W50) Brauer groups of schemes (14F22) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Localization and associative Noetherian rings (16P50) Generalizations (algebraic spaces, stacks) (14A20) Schemes and morphisms (14A15) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02) Abelian varieties and schemes (14Kxx) Rings with polynomial identity (16Rxx)

Related Items (20)

On strongly prime rings and ideals ⋮ Algebraic elements in division algebras over function fields of curves ⋮ The affine scheme associated to a non-Noetherian prime PI algebra ⋮ Geometry of free loci and factorization of noncommutative polynomials ⋮ Rings and sheaves ⋮ Quantum principal bundles on projective bases ⋮ On centered and integral homomorphisms ⋮ Obstructing extensions of the functor Spec to noncommutative rings ⋮ On compact generation of deformed schemes ⋮ Totally ordered sets and the prime spectra of rings ⋮ Noncommutative curves and noncommutative surfaces ⋮ Unicity for representations of the Kauffman bracket skein algebra ⋮ Noncommutative holomorphic functional calculus, affine and projective spaces from $\operatorname {NC}$-complete algebras ⋮ Cohomology of exact categories and (non-)additive sheaves ⋮ Noncommutative affine spaces and Lie-complete rings ⋮ Distortion of the Poisson bracket by the noncommutative Planck constants ⋮ Algebroid prestacks and deformations of ringed spaces ⋮ Extensions of integral domains and quasi-valuations ⋮ Noncommutative Localizations of Lie-Complete Rings ⋮ Quasi-valuations and algebras over valuation domains

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