Associative Algebraic Geometry
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€167.40
A01=Arvid Siqveland
Affine Associative Variety
Associative Algebraic Geometry
Author_Arvid Siqveland
Category=PBMW
Closed Points
Deformation Theory
Derivation
eq_isMigrated=1
eq_nobargain
Ext-Groups
Geometric Invariant Theory
Inductive Limits
Limits in Categories
Mathematical Models
Moduli
Multi-Local Rings
Multi-Local Stalk (of Sheaf of Ass. Alg.)
Noncommutative Algebraic Geometry
Phase Space
Projective Limits
Representation Theory
Sheaf of Associative Algebras
Simp
Simple Modules
Small Categories
Spec
Topology on Module Categories
Universal Properties
Product details
- ISBN 9781800613546
- Publication Date: 10 Mar 2023
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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Classical Deformation Theory is used for determining the completions of local rings of an eventual moduli space. When a moduli variety exists, the main result explored in the book is that the local ring in a closed point can be explicitly computed as an algebraization of the pro-representing hull, called the local formal moduli, of the deformation functor for the corresponding closed point.The book gives explicit computational methods and includes the most necessary prerequisites for understanding associative algebraic geometry. It focuses on the meaning and the place of deformation theory, resulting in a complete theory applicable to moduli theory. It answers the question 'why moduli theory', and gives examples in mathematical physics by looking at the universe as a moduli of molecules, thereby giving a meaning to most noncommutative theories.The book contains the first explicit definition of a noncommutative scheme, not necessarily covered by commutative rings. This definition does not contradict any previous abstract definitions of noncommutative algebraic geometry, but sheds interesting light on other theories, which is left for further investigation.
