Fields Medal Lecture: Period maps in p-adic geometry - Peter Scholze - ICM2018

Fields Medal Lecture / Plenary Lecture 9
Period maps in 𝑝-adic geometry
Peter Scholze
Abstract: We discuss recent developments in 𝑝-adic geometry, ranging from foundational results such as the degeneration of the Hodge-to-de Rham spectral sequence for “compact 𝑝-adic manifolds” over new period maps on moduli spaces of abelian varieties to applications to the local and global Langlands conjectures, and the construction of “universal” 𝑝-adic cohomology theories. We finish with some speculations on how a theory that combines all primes 𝑝, including the archimedean prime, might look like.
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