In joint work with Hélène we study certain pure l-adic local systems on varieties over p-adic local fields which are analogs of variations of pure Hodge structures. In the talk I will explain an approach via tilting to the most basic open problems in this setting: analogs of limiting mixed Hodge structures and purity of cohomology for a curve.
Moritz Kerz (Universität Regensburg)
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