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 3: The purpose of this talk is to discuss the moduli of B^+_dR-lattices with extra structure. We prove they are kimberlites in general and we sketch the proof of the representability by formal schemes of the “local models” attached to minuscule cocharacters. We introduce the notion of unibranch kimberlites and explain its relation to normality. We prove that these moduli spaces are unibranch.

Ian Gleason (Berkeley, USA)

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