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2-Gerbes and 2-Tate Spaces

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Arithmetic and Geometry Around Quantization

Part of the book series: Progress in Mathematics ((PM,volume 279))

Summary

We construct a central extension of the group of automorphisms of a 2-Tate vector space viewed as a discrete 2-group. This is done using an action of this 2-group on a 2-gerbe of gerbal theories. This central extension is used to define central extensions of double loop groups.

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References

  1. M. Artin, B. Mazur, Etale Homotopy, Lecture Notes in Mathematics 100, Springer-Verlag 1969.

    Google Scholar 

  2. A. A. Beilinson, How to glue perverse sheaves in: K-theory, Arithmatic and Geometry Editor: Y. I. Manin, Lecture Notes in Mathematics 1289, 42–51, Springer-Verlag 1987.

    Google Scholar 

  3. Benabou, Jean Introduction to bicategories. 1967 Reports of the Midwest Category Seminar pp. 1–77 Springer, Berlin.

    Google Scholar 

  4. Breen, Lawrence On the classification of 2-gerbes and 2-stacks. Astrisque No. 225 (1994).

    Google Scholar 

  5. Brylinski, Jean-Luc Central extensions and reciprocity laws. Cahiers Topologie Gom. Diffrentielle Catg. 38 (1997), no. 3, 193–215.

    Google Scholar 

  6. Drinfeld, Vladimir Infinite-dimensional vector bundles in algebraic geometry: an introduction. The unity of mathematics, 263–304, Progr. Math., 244, Birkhäuser Boston, Boston, MA, 2006.

    Google Scholar 

  7. Kato, Kazuya Existence theorem for higher local fields. Invitation to higher local fields (Mnster, 1999), 165–195 (electronic), Geom. Topol. Monogr., 3, Geom. Topol. Publ., Coventry, 2000.

    Google Scholar 

  8. Lurie, Jacob Higher topos theory. Annals of Mathematics Studies, 170. Princeton University Press, Princeton, NJ, 2009.

    Google Scholar 

  9. Osipov, D. V. Central extensions and reciprocity laws on algebraic surfaces. (Russian) Mat. Sb. 196 (2005), no. 10, 111–136; translation in Sb. Math. 196 (2005), no. 9–10, 1503–1527.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada

    Sergey Arkhipov

  2. Mathematical Institute, University of Oxford, Oxford, UK

    Kobi Kremnizer

Authors
  1. Sergey Arkhipov
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  2. Kobi Kremnizer
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Corresponding author

Correspondence to Sergey Arkhipov .

Editor information

Editors and Affiliations

  1. MPI fĂĽr Mathematik, Vivatsgasse 7, Bonn, 53111, Germany

    Özgür Ceyhan  & Yu. I. Manin  & 

  2. Department of Mathematics, California Institute of Technology, 1200 E . California Blvd., Pasadena, CA, 91125, USA

    Matilde Marcolli

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Arkhipov, S., Kremnizer, K. (2010). 2-Gerbes and 2-Tate Spaces. In: Ceyhan, Ö., Manin, Y.I., Marcolli, M. (eds) Arithmetic and Geometry Around Quantization. Progress in Mathematics, vol 279. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4831-2_2

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