Research

I study mathematics, specializing in analytic 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 Berkovich 2-motives and normed ring stacks, I characterize the stable presentable symmetric monoidal (∞, 2)-category of Berkovich 2-motives as freely generated by a ring stack equipped with an absolute value satisfying certain easy-to-verify conditions. A corrected version is available here on arXiv.

Preprints

All these works were written with submission to research journals in mind.

• The Oka principle for étale Chow groups.

  Ko Aoki.

  [arXiv:2609.09871]

• The decomposition relations alone present the Goncharov Lie coalgebra.

  Ko Aoki.

  [arXiv:2609.02307]

• Inaccessibility of the flat topology.

  Ko Aoki and Robert Burklund.

  [arXiv:2607.09440]

• Berkovich 2-motives and normed ring stacks.

  Ko Aoki.

  [arXiv:2603.01877]

• Higher presentable categories and limits.

  Ko Aoki.

  [arXiv:2510.13503]

• Higher Zariski geometry.

  Ko Aoki, Tobias Barthel, Anish Chedalavada, Tomer Schlank, and Greg Stevenson.

  [arXiv:2508.11621]

• Very Schwartz coidempotents and continuous spectrum.

  Ko Aoki.

  [arXiv:2505.04817]

• 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]

Peer-reviewed papers

• On cohomology of locally profinite sets.

  Ko Aoki.

  Proc. London Math. Soc. (3) 132 (2026), e70159.

  [arXiv:2411.05995] [doi:10.1112/plms.70159]

• K-theory of rings of continuous functions.

  Ko Aoki.

  Camb. J. Math. 14 (2026), no. 2, 243–283.

  [arXiv:2402.05257] [doi:10.4310/CJM.260514222021]

• The sheaves–spectrum adjunction.

  Ko Aoki.

  Mathematische Annalen 396 (2026), no. 2, 30.

  [arXiv:2302.04069] [doi:10.1007/s00208-026-03545-y]

• 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

• Toposes in gestalten. Extended abstract of my talk at the Oberwolfach miniworkshop on gestalten, 2026.
• Berkovich 2-motives and normed ring stacks. Extended abstract of my talk at the Oberwolfach workshop on algebraic K-theory, 2025.
• 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.