Research

In their recent paper, Annala–Pstrągowski construct a weight filtration on $\mathrm{kgl}$-linear cohomology theories over resolvable motives. However, working with these filtrations (in particular, showing that certain comparison maps are functorial) is difficult within the constraints of the construction. I am working on describing the $\infty$-category $\mathrm{DM}^{\mathrm{kgl}}_{S,\mathrm{res}}$ of $\mathrm{kgl}$-linear resolvable motives in terms of only smooth log smooth projective schemes, which, using logarithmic geometry, would make it easier to define functors out of this $\infty$-category.

With this description in hand, it should be relatively straightforward to e.g. recover Mokrane’s décalaged pole-order filtration on logarithmic crystalline cohomology.