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.

PhD thesis

In my thesis (in preparation), I characterize the 2-category of Berkovich 2-motives as the one freely generated by a normed ring stack satisfying certain easy-to-verify conditions.

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.