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Uniformization of semistable bundles on ...
Li, Penghui...

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Uniformization of semistable bundles on elliptic curves by Li, Penghui ( Author )
Lemonjar Open Access
N.A
02-08-2023
Let $G$ be a connected reductive complex algebraic group, and $E$ a complex elliptic curve. Let $G_E$ denote the connected component of the trivial bundle in the stack of semistable $G$-bundles 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 \simeq \mathbb{C}^*/q^{\mathbb{Z}}$. We similarly construct a complex analytic uniformization of $G$ itself via the exponential map, providing a nonabelian version of the standard isomorphism $\mathbb{C}^* \simeq \mathbb{C}/\mathbb{Z}$, and a complex analytic uniformization of $G_E$ generalizing the standard presentation $E = \mathbb{C}/(\mathbb{Z} \oplus \mathbb{Z} \tau )$. 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 $Sh_\mathcal{N}(G_E)$ (the semistable part of the automorphic category) to ${IndCoh}_{\check{\mathcal{N}}}({Locsys}_{\check G} (E))$ (the spectral category).
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Article
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37.08 KB
English
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MYR 0.01
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http://arxiv.org/abs/1510.08762
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