Skip to main content
SpringerLink
Log in

A Quasi-Coherent Description of the Category D -mod(GrGL(n))

  • Chapter
  • First Online:
Representation Theory and Algebraic Geometry

Part of the book series: Trends in Mathematics ((TM))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In this case, the equivalence actually holds on the level of abelian categories, but the equivalence of Conjecture 3 only has a chance to hold on the derived level. Also in this case, there is no difference between QCoh and IndCoh.

  2. 2.

    Here \(\pi ^{-1}(\operatorname {\mathcal E})\) should be understood in dg-sense.

  3. 3.

    Here when we write Λ(W[d]) (for a vector space W and \(d\in \mathbb {Z}\)), we just mean the dg-algebra with trivial differential which is equal to the exterior algebra generated by elements of W which have homological degree − d, i.e., we are NOT using the “super-notation” here with respect to the homological degree. Same goes for the notation \({ \mathop {\operatorname {\mathrm {Sym}}}}(W[d])\).

References

  1. D. Arinkin and D. Gaitsgory, Singular support of coherent sheaves, and the geometric Langlands conjecture, Selecta Math. (N.S.) 21 (2015), no. 1, 1–199.

    Google Scholar 

  2. R. Bezrukavnikov, M. Finkelberg, Equivariant Satake category and Kostant-Whittaker reduction, Moscow Math. J. 8 (2008), no. 1, 39–72.

    Article  MathSciNet  Google Scholar 

  3. A. Braverman and M. Finkelberg, Coulomb branches of 3-dimensional gauge theories and related structures, Lecture Notes in Mathematics 2248 (2019), 1–52.

    Article  MathSciNet  Google Scholar 

  4. V. Drinfeld and D. Gaitsgory, On some finiteness questions for algebraic stacks, Geom. Funct. Anal. 23 (2013), no. 1, 149–294.

    Article  MathSciNet  Google Scholar 

  5. D. Gaitsgory, Progrès récents dans la théorie de Langlands géométrique, Séminaire Bourbaki, Astérisque 390 (2017), exp. no. 1109, 139–168; arXiv:1606.09462.

    Google Scholar 

  6. V. Ginzburg, Perverse sheaves and\(\mathbb C^*\)-actions, J. Amer. Math. Soc. 4 no. 3 (1991), 483–490.

    Google Scholar 

  7. G. Laumon, Transformation de Fourier généralisée, alg-geom/9603004.

    Google Scholar 

Download references

Acknowledgements

This paper resulted from numerous conversations of the first-named author with D. Gaitsgory and S. Raskin which took place during the workshop “Vertex algebras, factorization algebras and applications” at IPMU in July 2018. The authors thank both D. Gaitsgory and S. Raskin for their patient explanations and the organizers of the workshop for hospitality and for providing this opportunity. We would also like to thank Roman Bezrukavnikov for help with some technical details of the proof. M.F. was partially funded within the framework of the HSE University Basic Research Program and the Russian Academic Excellence Project ‘5-100’.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto and Perimeter Institute of Theoretical Physics, Waterloo, ON, Canada

    Alexander Braverman

  2. Skolkovo Institute of Science and Technology, Moscow, Russia

    Alexander Braverman

  3. Department of Mathematics, National Research University Higher School of Economics, Russian Federation, Moscow, Russia

    Michael Finkelberg

  4. Skolkovo Institute of Science and Technology, Institute for Information Transmission Problems of RAS, Moscow, Russia

    Michael Finkelberg

Authors
  1. Alexander Braverman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Finkelberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Braverman .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, Irvine, Irvine, CA, USA

    Vladimir Baranovsky

  2. Department of Math. & Stat. Sciences, University of Alberta, Edmonton, AB, Canada

    Nicolas Guay

  3. Department of Mathematics, Imperial College London, London, UK

    Travis Schedler

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Braverman, A., Finkelberg, M. (2022). A Quasi-Coherent Description of the Category D -mod(GrGL(n)). In: Baranovsky, V., Guay, N., Schedler, T. (eds) Representation Theory and Algebraic Geometry. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-82007-7_5

Download citation

Publish with us

Policies and ethics

Search

Navigation