The global nilpotent cone is the zero fiber of the Hitchin map in the moduli space of Higgs bundles over an algebraic curve. It is a conic Lagrangian in the ambient symplectic moduli space, and it plays an important role in the geometric Langlands program. In this talk we define a version of the global nilpotent cone for a family of curves. It will be a closed conic Lagrangian in the cotangent bundle of the total space of the family of Bun_G's for the family of curves. Implicitly it encodes a "connection" among the category of sheaves on Bun_G as the curve varies. I will mention the motivation of the construction from Betti geometric Langlands. This is joint work with David Nadler.

Notes: https://seafile.ist.ac.at/f/4a298acb2afe4d648e89