11 papers
On motivic cohomology of commutative C*-algebras
Ko Aoki
Consider the ring of complex-valued continuous functions on a compact Hausdorff space . Cortiñas--Thom computed its nonpositive algebraic -theory, confirming Rosenberg's expe…
The Oka principle for étale Chow groups
Ko Aoki
The celebrated theorems of Shilov, Arens--Royden, and Forster give direct descriptions of the first three integral cohomology groups of the Gelfand spectrum of a commutative comple…
The decomposition relations alone present the Goncharov Lie coalgebra
Ko Aoki
Recently, Kupers--Rudenko--Sierra introduced the Goncharov Lie coalgebra. They gave a presentation using correlator generators and four types of relations: homogeneity, cyclic symm…
Inaccessibility of the flat topology
Ko Aoki, Robert Burklund
We prove that singleton covers in the flat topology on affine schemes are not closed under -cofiltered limits for any regular cardinal . Therefore, for every accessible flat…
Berkovich -motives and normed ring stacks
Ko Aoki
The de Rham stack construction of Simpson shows that D-modules are quasicoherent sheaves on a modified geometry. Drinfeld furthermore introduced the ring stack perspective (aka tra…
Higher presentable categories and limits
Ko Aoki
Stefanich generalized the notion of (locally) presentable -category to the notion of presentable -category. We give a new description based on the new not…
Higher Zariski Geometry
Ko Aoki, Tobias Barthel, Anish Chedalavada +2
We revisit the classical constructions of tensor-triangular geometry in the setting of stably symmetric monoidal idempotent-complete -categories, henceforth referred to as…
Very Schwartz coidempotents and continuous spectrum
Ko Aoki
We introduce the continuous version of the (unstable) smashing spectrum functor. In the stable case, it assigns to each dualizably symmetric monoidal stable presentable -ca…
On cohomology of locally profinite sets
Ko Aoki
We construct a locally profinite set of cardinality with infinitely many first cohomology classes of which any distinct finite product does not vanish. Building on this,…
(Semi)topological -theory via solidification
Ko Aoki
Clausen--Scholze introduced the notion of solid spectrum in their condensed mathematics program. We demonstrate that the solidification of algebraic -theory recovers two known c…
The smashing spectrum of sheaves
Ko Aoki
For an arbitrary -topos, we classify the smashing localizations in the -category of sheaves valued in derived vector spaces: Any of them is the restriction functor…