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
https://eta.impa.br/dl/PL016.pdf
https://arxiv.org/abs/1712.03708
本文讨论p进几何，两大主题是代数簇的上同调和局部与整体Langlands对应。首先回顾p进Hodge理论，并讨论分别来自于de Rham上同调和平展上同调的周期映射。然后给出应用：构造相应于一般线性群GL(n)的局部对称流形（例如：双曲三维流形）的Galois表示。作者考虑Drinfeld的штука的p进类比，并试图理解万有上同调理论在多大程度上可以由相对于Spec Z的一个штука给出。
相关附件
9-PL016 Scholze
