Free factorization algebras and homology of configuration spaces in algebraic geometry. (English) Zbl 1422.55030
Summary: We provide a construction of free factorization algebras in algebraic geometry and link factorization homology of a scheme with coefficients in a free factorization algebra to the homology of its (unordered) configuration spaces. As an application, this construction allows for a purely algebro-geometric proof of homological stability of configuration spaces.
MSC:
| 55R80 | Discriminantal varieties and configuration spaces in algebraic topology |
| 14A20 | Generalizations (algebraic spaces, stacks) |
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 17B56 | Cohomology of Lie (super)algebras |
| 18G55 | Nonabelian homotopical algebra (MSC2010) |
| 81R99 | Groups and algebras in quantum theory |
Keywords:
chiral algebras; chiral homology; factorization algebras; Koszul duality; homological stability; configuration spacesReferences:
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