For $\ell$-adic cohomology, the weight monodromy conjecture for complete intersections was proved by Scholze in his celebrated paper. Using his theory of perfectoid spaces, he reduced it to the equal characteristic case, which was already proved by Deligne. Considering that the equal characteristic case of the p-adic weight monodromy conjecture has been also formulated and proved (by Crew and Lazda--Pal), it is natural to try to reduce the p-adic weight monodromy conjecture to the equal characteristic case using Scholze's technique. In this talk, I will discuss how to realize it (joint work with Federico Binda and Alberto Vezzani).
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Ahmed Abbes
