talk maths, formerly >>9837232
picture from https://arxiv.org/pdf/1712.03708.pdf
>p-adic geometry
>Peter Scholze
>(Submitted on 11 Dec 2017)
>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.
picture from https://arxiv.org/pdf/1712.03708.pdf
>p-adic geometry
>Peter Scholze
>(Submitted on 11 Dec 2017)
>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.
