Exposés de recherche

Collection Exposés de recherche

00:00:00 / 00:00:00
350 380

​On the motive of the stack of vector bundles on a curve

By Victoria Hoskins

Also appears in collection : Gauge theory and complex geometry / ​Théorie de jauge et géométrie complexe

Following Grothendieck’s vision that a motive of an algebraic variety should capture many of its cohomological invariants, Voevodsky introduced a triangulated category of motives which partially realises this idea. After describing some of the properties of this category, I explain how to define the motive of certain algebraic stacks. I will then focus on defining and studying the motive of the moduli stack of vector bundles on a smooth projective curve and show that this motive can be described in terms of the motive of this curve and its symmetric powers. If there is time, I will give a conjectural formula for this motive, and explain how this follows from a conjecture on the intersection theory of certain Quot schemes. This is joint work with Simon Pepin Lehalleur.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19417003
  • Cite this video Hoskins, Victoria (19/06/2018). ​On the motive of the stack of vector bundles on a curve. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19417003
  • URL https://dx.doi.org/10.24350/CIRM.V.19417003

Domain(s)

Bibliography

  • Hoskins, V., Pepin Lehalleur, S. (2017). On the Voevodsky motive of the moduli stack of vector bundles on a curve. <arXiv:1711.11072> - https://arxiv.org/abs/1711.11072

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback