Research

I study mathematics, specializing in arithmetic geometry. I primarily focus on K-theory, spectral methods, and (∞, n)-categories. I recently introduced the notion of n-rigidity for presentable (∞, n)-categories and am working on constructing an example related to K-theory—noncommutative n-motives.

Preprints

Certain databases list some preprints as “submitted,” but this is not always accurate. Nevertheless, all these works were written with submission to research journals in mind.

Very Schwartz coidempotents and continuous spectrum.
Ko Aoki.
[arXiv:2505.04817]
On cohomology of locally profinite sets.
Ko Aoki.
[arXiv:2411.05995]
Rosenberg’s conjecture for the first negative K-group.
Ko Aoki.
[arXiv:2409.09651]
(Semi)topological K-theory via solidification.
Ko Aoki.
[arXiv:2409.01462]
The smashing spectrum of sheaves.
Ko Aoki.
[arXiv:2406.03969]
K-theory of rings of continuous functions.
Ko Aoki.
[arXiv:2402.05257]
The sheaves–spectrum adjunction.
Ko Aoki.
[arXiv:2302.04069]

Peer-reviewed papers

Posets for which Verdier duality holds.
Ko Aoki.
Selecta Math. (N.S.) 29 (2023), Paper No. 78, 22 pp.
[arXiv:2202.05312] [doi:10.1007/s00029-023-00887-2]
Quasiexcellence implies strong generation.
Ko Aoki.
J. Reine Angew. Math. 780 (2021), 133–138.
[arXiv:2009.02013] [doi:10.1515/crelle-2021-0034]
Tensor triangular geometry of filtered objects and sheaves.
Ko Aoki.
Math. Z. 303 (2023), no. 3, Paper No. 62, 27 pp.
[arXiv:2001.00319] [doi:10.1007/s00209-023-03210-z]
The weight complex functor is symmetric monoidal.
Ko Aoki.
Advances in Mathematics 368 (2020), 107145, 10 pp.
[arXiv:1904.01384] [doi:10.1016/j.aim.2020.107145]

Talks

A list of research talks is available here.

Reports

A 2-rigid 2-category of 2-motives. Poster at the BIGS poster exhibition, 2025.
Presentable (∞, n)-categories. Poster at the BIGS poster exhibition, 2024.
Analytic K-theory. Poster at the BIGS poster exhibition, 2023.
Analytic K-theory (progress report). Poster at the BIGS poster exhibition, 2022.