Skip to main content
SpringerLink
Log in

Brauer class over the Picard scheme of totally degenerate stable curves

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

Abstract

We study the Brauer class rising from the obstruction to the existence of tautological line bundles on the Picard scheme of curves. We determine the period and index of that Brauer class in certain cases.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. This is only needed when we consider loops with 2 vertices, otherwise there is only one edge.

References

  1. Auel, Asher, Brussel, Eric, Garibaldi, Skip, Vishne, Uzi: Open problems on central simple algebras. Transform. Groups 16(1), 219–264 (2011)

    Article  MathSciNet  Google Scholar 

  2. Arbarello, Enrico, Cornalba, Maurizio, Griffiths, Phillip: Geometry of algebraic curves: volume II with a contribution by Joseph Daniel Harris, vol. 268. Springer Science & Business Media, Berlin (2011)

    Book  Google Scholar 

  3. Antieau, Benjamin, Williams, Ben: The period-index problem for twisted topological \(k\!\)-theory. Geom. Topol. 18(2), 1115–1148 (2014)

    Article  MathSciNet  Google Scholar 

  4. Antieau, Benjamin, Williams, Ben: The topological period-index problem over 6-complexes. J. Topol. 7(3), 617–640 (2014)

    Article  MathSciNet  Google Scholar 

  5. Bosch, Siegfried: Néron Models. Springer, Berlin Heidelberg, Berlin, Heidelberg (1990)

    Book  Google Scholar 

  6. Giraud, J.: Cohomologie non abelienne. Springer-Verlag, Berlin, New York (1971)

    Book  Google Scholar 

  7. Gille, Philippe, Szamuely, Tamás: Central simple algebras and Galois cohomology, vol. 165. Cambridge University Press, Cambridge (2017)

    Book  Google Scholar 

  8. Milne, J.S.: Algebraic groups : the theory of group schemes of finite type over a field. Cambridge University Press, Cambridge, United Kingdom New York, New York (2017)

    Book  Google Scholar 

  9. Rowen, Louis H., Saltman, David J.: Dihedral algebras are cyclic. Proc. Am. Math Soc. 84(2), 162–164 (1982)

    Article  MathSciNet  Google Scholar 

  10. Skorobogatov, A.N.: On the elementary obstruction to the existence of rational points. Mat. Zametki 81(1), 112–124 (2007)

    Article  MathSciNet  Google Scholar 

  11. The Stacks Project Authors. Stacks Project. https://stacks.math.columbia.edu, (2018)

Download references

Acknowledgements

This work is a part of my thesis at Columbia University. I am very grateful to my advisor Aise Johan de Jong for his invaluable ideas, enlightening discussions and unceasing encouragement. I am also very grateful to the 2018 Brauer Group conference, where I first had chance to present this work and got warmly encouraged by many people. I heartily thank the anonymous referee for the very careful proofreading, and helping me clarifying the proof of Proposition 3.5.

Author information

Authors and Affiliations

  1. Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China

    Qixiao Ma

Authors
  1. Qixiao Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qixiao Ma.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, Q. Brauer class over the Picard scheme of totally degenerate stable curves. Math. Z. 298, 1641–1652 (2021). https://doi.org/10.1007/s00209-020-02663-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-020-02663-w

Search

Navigation