Symplectic, or mirrorical, look at the Fargues-Fontaine curve
David Treuman (Boston College)
Title: Symplectic, or mirrorical, look at the Fargues-Fontaine curve
Abstract: Homological mirror symmetry describes Lagrangian Floer theory on a torus in terms of vector bundles on the Tate elliptic curve. A version of Lekili and Perutz's works "over Z[[t]]", where t is the Novikov parameter. I will review this story and describe a modified form of it, which is joint work with Lekili, where the Floer theory is altered by a locally constant sheaf of rings on the torus. When the fiber of this sheaf of rings is perfectoid of characteristic p, and the holonomy around one of the circles in the torus is the pth power map, it is possible to specialize to t = 1, and the resulting theory there is described in terms of vector bundles on the equal-characteristic-version of the Fargues-Fontaine curve.
Recording taken from the Arithmetic Geometry and Quantum Field Theory seminar, organised by Jeff Harvey and Minhyong Kim