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 2: The purpose of this talk is to discuss the theory of kimberlites. We introduce the reduction functor, specializing sheaves, prekimberlites, kimberlites, tubular and etale neighborhoods. We discuss the topological specialization map and the v-sheaf theoretic specialization map. We discuss the etale site of a prekimberlite, the formal and analytic nearby cycles functors and the comparison between them. We discuss finiteness condtions and the specialization triples principle.

Ian Gleason (Berkeley, USA)

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