Publications

  1. Every motive is the motive of a stable $\infty$-category.
    joint with Maxime Ramzi and Christoph Winges
    arxiv
  2. On filtered algebraic K-theory of stacks I: characteristic zero. preprint
    joint with Elden Elmanto and Dmitry Kubrak
    arxiv
  3. Every spectrum is the K-theory of a stable $\infty$-category. preprint
    joint with Maxime Ramzi and Christoph Winges
    arxiv
  4. $\mathbb{A}^1$-invariance of localizing invariants. Annals of K-theory, 9 (2024)
    arxiv
    journal
  5. Categorical Milnor squares and K-theory of algebraic stacks. Selecta Mathematica, 28 (2022)
    joint with Tom Bachmann, Adeel A. Khan and Charanya Ravi
    Warning: Lemma 3.5.5 contains a gap This means that currently we can only show that the squares appearing in Theorems A, B and C are weakly cartesian and not cartesian. In Theorem 3.5.11 we have to assume that the localizing invariant is connected in the sense of Land-Tamme. The statements for connected invariants and the proofs that do not rely on this lemma can be found in my thesis
    arxiv
    journal
  6. Zariski-local framed $\mathbb{A}^1$-homotopy theory. preprint
    joint with Andrei Druzhinin
    arxiv
  7. On nilpotent extensions of $\infty$-categories and the cyclotomic trace. International Mathematics Research Notices, 21 (2022)
    joint with Elden Elmanto
    arxiv
    journal
  8. On Chow-weight homology of geometric motives. Transactions of the AMS, 375 (2022)
    joint with Mikhail Bondarko
    arxiv
    journal
  9. Regularity of spectral stacks and discreteness of weight-hearts. Quarterly Journal of Mathematics, 73 (2022)
    arxiv
    journal
  10. Motivic infinite loop spaces. Cambridge Journal of Mathematics, 9 (2021)
    joint with Elden Elmanto, Marc Hoyois, Adeel A. Khan and Maria Yakerson
    arxiv
    journal
  11. On the infinite loop spaces of algebraic cobordism and the motivic sphere. Épijournal Géom. Algébrique, 5 (2021)
    joint with Tom Bachmann, Elden Elmanto, Marc Hoyois, Adeel A. Khan and Maria Yakerson
    arxiv
    journal
  12. Modules over algebraic cobordism. Forum of Mathematics, $\Pi$, 8 (2021)
    joint with Elden Elmanto, Marc Hoyois, Adeel A. Khan and Maria Yakerson
    arxiv
    journal
  13. Framed transfers and motivic fundamental classes. Journal of Topology, 13 (2020)
    joint with Elden Elmanto, Marc Hoyois, Adeel A. Khan and Maria Yakerson
    arxiv
    journal
  14. Theorem of the heart in negative K-theory for weight structures. Documenta Mathematica, 24 (2019)
    arxiv
    journal
  15. On purely generated $\alpha$-smashing weight structures and weight-exact localizations. Journal of Algebra, 535 (2019)
    joint with Mikhail Bondarko
    arxiv
    journal
  16. Higher colimits, derived functors and homology. Sbornik Mathematics, 210 (2019)
    joint with Sergei O. Ivanov, Roman Mikhailov
    arxiv
    journal
  17. On the weight lifting property for localizations of triangulated categories. Lobachevskii Journal of Mathematics, 39 (2018)
    joint with Mikhail Bondarko
    arxiv
    journal
  18. On constructing weight structures and extending them to idempotent extensions. Homology, Homotopy and Applications, 20 (2018)
    joint with Mikhail Bondarko
    arxiv
    journal
  19. Non-commutative localizations of additive categories and weight structures; applications to birational motives. Journal of the Institute of Mathematics of Jussieu, 17 (2016)
    joint with Mikhail Bondarko
    arxiv
    journal
  20. A Nullstellensatz for triangulated categories. Algebra and Analysis, 27 (2015)
    joint with Mikhail Bondarko
    arxiv
    journal

PhD thesis

  1. Weighted methods in noncommutative geometry.
    pdf