Quantizing Deformation Theory II
نویسندگان
چکیده
منابع مشابه
Quantizing deformation theory
We describe a step toward quantizing deformation theory. The L∞ operad is encoded in a Hochschild cocyle ◦1 in a simple universal algebra (P, ◦0). This Hochschild cocyle can be extended naturally to a star product ⋆ = ◦0+~◦1+~ 2 ◦2+ · · · . The algebraic structure encoded in ⋆ is the properad Ω(coFrob) which, conjecturally, controls a quantization of deformation theory—a theory for which Froben...
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In mathematical deformation theory one studies how an object in a certain category of spaces can be varied in dependence of the points of a parameter space. In other words, deformation theory thus deals with the structure of families of objects like varieties, singularities, vector bundles, coherent sheaves, algebras or differentiable maps. Deformation problems appear in various areas of mathem...
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In these notes we’ll give an introduction to deformation theory and apply it to the special case of abelian schemes. We’ll start by defining the deformation functor and show how the cohomology groups of the sheaf of derivations of a scheme can be used to both determine if deformations exist and if so, what the set of deformations looks like. After that, we’ll introduce the 800 pound gorilla of ...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2020
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2020.v16.n1.a3