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The study of harmonic differential forms on complex projective varieties, their invariantly defined filtrations, their integrals over topological cycles, especially over subvarieties, the deformations of these integrals and filtrations in families, and a multitude of generalizations.
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Arakelov Motivic Cohomology and Hodge Theory
Lately I have been studying these two papers (first and second) that introduce a new cohomology theory called Arakelov motivic cohomology. While most of the applications presented in the papers are fr …