Looking for a category to represent Hodge filtration, with or without log, with or without modulus.
Using a geometric definition of logarithmic Hochschild homology of derived pre-log rings, we construct an André-Quillen type spectral sequence and show a logarithmic version of the Hochschild-Kostant-Rosenberg theorem. We use this to show that (log) Hochschild homology is representable in the category of log motives. Among the applications, we deduce a residue sequence for Hochschild homology...
Binda-Rulling-Saito proved that a smooth proper variety with universally trivial Chow group of zero-cycles has trivial unramified cohomology for any reciprocity sheaves.
We generalize this result to P^1-invariant sheaves with transfers. A key ingredient is a new moving lemma.
This is joint work with Wataru Kai and Shusuke Otabe.
