The global nilpotent cone for universal curves

David Nadler; Zhiwei Yun

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arXiv · 2603.01261

The global nilpotent cone for universal curves

David Nadler·Zhiwei Yun

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Abstract

We construct a conic Lagrangian in the cotangent bundle of the moduli stack of $G$-bundles over the universal curve, restricting to the global nilpotent cone for each curve. It gives rise to a singular support condition suitable for the Betti geometric Langlands correspondence for families of curves and the automorphic gluing functor studied in arXiv: 2105.12318. We also prove a family version of ``local constancy of Hecke operators," generalizing our earlier result.

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David Nadler, Zhiwei Yun. 2026-03-01. The global nilpotent cone for universal curves. https://arxiv.org/abs/2603.01261

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