Uniformization of semistable bundles on elliptic curves

Penghui Li YMSC, Tsinghua University David Nadler University of California, Berkeley

Representation Theory mathscidoc:2205.30001

Advances in Mathematics, 380, 107572, 2021.3
Let G be a connected reductive complex algebraic group, and E a complex elliptic curve. Let GE denote the connected component of the trivial bundle in the stack of semistable Gbundles on E. We introduce a complex analytic uniformization of G_E by adjoint quotients of reductive subgroups of the loop group of G. This can be viewed as a nonabelian version of the classical complex analytic uniformization E=C^∗/q^Z. We similarly construct a complex analytic uniformization of G itself via the exponential map, providing a nonabelian version of the standard isomorphism C^∗= C/Z, and a complex analytic uniformization of G_E generalizing the standard presentation E = C/(Z ⊕ Zτ). Finally, we apply these results to the study of sheaves with nilpotent singular support. As an application to Betti geometric Langlands conjecture in genus 1, we define a functor from Sh_N(G_E) (the semistable part of the automorphic category) to IndCoh_{Nˇ}(Locsys_{Gˇ}(E)) (the spectral category).
No keywords uploaded!
[ Download ] [ 2022-05-18 15:00:20 uploaded by PenghuiLi ] [ 51 downloads ] [ 0 comments ]
@inproceedings{penghui2021uniformization,
  title={Uniformization of semistable bundles on elliptic curves},
  author={Penghui Li, and David Nadler},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220518150020614651268},
  booktitle={Advances in Mathematics},
  volume={380},
  pages={107572},
  year={2021},
}
Penghui Li, and David Nadler. Uniformization of semistable bundles on elliptic curves. 2021. Vol. 380. In Advances in Mathematics. pp.107572. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220518150020614651268.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved