Yicheng Zhou (Paris-Saclay)

For a “large” class of rigid-analytic varieties over a p-adic local field, we explain how to construct a natural syntomic descent spectral sequence compatible with the Hochschild-Serre spectral sequence. As a consequence, for proper rigid-analytic varieties, the étale regulators maps on suitable K-theoretic groups factor through their syntomic counterparts, for suitably defined syntomic Chern class maps.