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Free factorization algebras and homology of configuration spaces in algebraic geometry

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Abstract

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.

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References

  1. Ayala, D., Francis, J.: Factorization homology of topological manifolds (2012). arXiv:1206.5522

  2. Ayala, D., Francis, J.: Poincaré/Koszul duality (2014). arXiv:1409.2478

  3. Beilinson, A., Drinfeld, V.: Chiral Algebras. American Mathematical Society Colloquium Publications, vol. 51, American Mathematical Society, Providence, RI, MR2058353

  4. Francis, J., Gaitsgory, D.: Chiral koszul duality (March 29, 2011). Selecta Math. (N.S.) 18(1), 27–87 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Farb, B., Wolfson, J.: Etale homological stability and arithmetic statistics (2015). arXiv:1512.00415

  6. Gaitsgory, D.: The Atiyah-Bott formula for the cohomology of the moduli space of bundles on a curve (2015). arXiv:1505.02331

  7. Getzler, E.: Resolving mixed Hodge modules on configuration spaces. Duke. Math. J. 96(1), 175–203 (1999). MR1663927

    Article  MathSciNet  MATH  Google Scholar 

  8. Ginzburg, V., Kapranov, M.: Koszul duality for operads. Duke. Math. J. 76(1), 203–272 (1994). MR1301191

  9. Gaitsgory, D., Lurie, J.: Weil’s conjecture for function fields (2014). http://www.math.harvard.edu/~lurie/. Accessed 10 Apr 2017

  10. Gaitsgory, D., Rozenblyum, N.: A study in derived algebraic geometry. To appear as part of the Mathematical Surveys and Monographs series, vol. 221. http://www.math.harvard.edu/~gaitsgde/GL/. Accessed 10 Apr 2017

  11. Kriz, I., May J.P.: Operads, algebras, modules and motives. Société mathématique de France (1995)

  12. Kupers, A., Miller, J.: \(E_n\)-cell attachments and a local-to-global principle for homological stability (2014). arXiv:1405.7087

  13. Kupers, A., Miller, J.: Homological stability for topological chiral homology of completions. Adv. Math. 292, 755–827 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  14. Knudsen, B.: Betti numbers and stability for configuration spaces via factorization homology (2014). arXiv:1405.6696

  15. Lurie, J.: Higher algebra. http://www.math.harvard.edu/~lurie/. Accessed 10 Apr 2017

  16. Lurie, J.: Higher topos theory. Annals of mathematics studies, vol. 170, Princeton University Press, Princeton, NJ (2009)

  17. Liu, Y., Zheng, W.: Enhanced adic formalism and perverse \(t\)-structures for higher artin stacks (2014). arXiv:1211.5948v2

  18. Liu, Y., Zheng, W.: Enhanced six operations and base change theorem for artin stacks (2012). arXiv:1211.5948

  19. Manetti, M.: On some formality criteria for DG-lie algebras. J. Algebra. 438, 90–118 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  20. Quillen, D.: Rational homotopy theory. Ann. Math. 90(2), 205–295 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  21. Raskin, S.: Chiral categories (2015). http://math.mit.edu/~sraskin/. Accessed 10 Apr 2017

  22. Totaro, B.: Configuration spaces of algebraic varieties. Topology. 35(4), 1057–1067 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Q. P. Hồ

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  1. Q. P. Hồ
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Hồ, Q.P. Free factorization algebras and homology of configuration spaces in algebraic geometry. Sel. Math. New Ser. 23, 2437–2489 (2017). https://doi.org/10.1007/s00029-017-0339-1

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