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Motivic six-functor formalism for log schemes

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arxiv 2403.07645 v2 pith:NGHZVC24 submitted 2024-03-12 math.AG

Doosung Park This is my paper · ORCID
classification math.AG
keywords schemesmotivicchowformalismhomologysix-functorbaseborel-moore
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We establish the motivic six-functor formalism for fs log schemes. In particular, we prove the exact base change property, projection formula, and Poincar\'e duality. We also define Borel-Moore motivic homology, G-theory, and Chow homology of fs log schemes and the category of Chow motives over fs log schemes.

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  1. The motivic fundamental groupoid at tangential basepoints

    math.AG 2025-10 conditional novelty 8.0 of 10

    A general motivic fundamental groupoid at tangential basepoints is constructed over any field, with Betti and de Rham realizations matching the classical fundamental torsor and periods given by regularized iterated integrals.

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