Seminar on Arithmetic Geometry

In this lecture series we aim to introduce the audience to the theory of kimberlites and its applications. The theory of kimberlites attempts to single out within Scholze’s category of v-sheaves those objects that “behave” as formal schemes. In this way, kimberlites provide well-behaved candidates for integral models of locally spatial diamonds. In the first two talks we discuss the foundations of the theory, and in the second two talks we discuss its applications to study moduli spaces of B_dR-lattices and moduli spaces of p-adic shtukas.

Talk 4: The purpose of this talk is to discuss the moduli of p-adic shtukas. We prove these moduli spaces are smelted kimberlites and single out the difficulties to proving that they are kimberlites. We discuss the v-sheaf theoretic “local diagram correspondence” for tubular neighborhoods relating moduli spaces of shtukas to moduli of B^+_dR-lattices. We prove they are unibranch. Finally we expalin how this is used to compute their connected components.

Ian Gleason (Berkeley, USA)

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