Publications

  1. $\mathbb{A}^1$-invariance of localizing invariants. To appear in Annals of K-theory
    arxiv
  2. Categorical Milnor squares and K-theory of algebraic stacks. Selecta Mathematica, 28 (2022)
    joint with Tom Bachmann, Adeel A. Khan and Charanya Ravi
    arxiv
    journal
  3. On nilpotent extensions of $\infty$-categories and the cyclotomic trace. International Mathematics Research Notices, 21 (2022)
    joint with Elden Elmanto
    arxiv
    journal
  4. On Chow-weight homology of geometric motives. Transactions of the AMS, 375 (2022)
    joint with Mikhail Bondarko
    arxiv
    journal
  5. Regularity of spectral stacks and discreteness of weight-hearts. Quarterly Journal of Mathematics, 73 (2022)
    arxiv
    journal
  6. Motivic infinite loop spaces. Cambridge Journal of Mathematics, 9 (2021)
    joint with Elden Elmanto, Marc Hoyois, Adeel A. Khan and Maria Yakerson
    arxiv
    journal
  7. 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
  8. Modules over algebraic cobordism. Forum of Mathematics, $\Pi$, 8 (2021)
    joint with Elden Elmanto, Marc Hoyois, Adeel A. Khan and Maria Yakerson
    arxiv
    journal
  9. 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
  10. Theorem of the heart in negative K-theory for weight structures. Documenta Mathematica, 24 (2019)
    arxiv
    journal
  11. On purely generated $\alpha$-smashing weight structures and weight-exact localizations. Journal of Algebra, 535 (2019)
    joint with Mikhail Bondarko
    arxiv
    journal
  12. Higher colimits, derived functors and homology. Sbornik Mathematics, 210 (2019)
    joint with Sergei O. Ivanov, Roman Mikhailov
    arxiv
    journal
  13. On the weight lifting property for localizations of triangulated categories. Lobachevskii Journal of Mathematics, 39 (2018)
    joint with Mikhail Bondarko
    arxiv
    journal
  14. On constructing weight structures and extending them to idempotent extensions. Homology, Homotopy and Applications, 20 (2018)
    joint with Mikhail Bondarko
    arxiv
    journal
  15. 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
  16. A Nullstellensatz for triangulated categories. Algebra and Analysis, 27 (2015)
    joint with Mikhail Bondarko
    arxiv
    journal

Preprints

  1. Every spectrum is the K-theory of a stable $\infty$-category.
    joint with Maxime Ramzi and Christoph Winges
    arxiv
  2. Zariski-local framed $\mathbb{A}^1$-homotopy theory.
    joint with Andrei Druzhinin
    arxiv

PhD thesis

  1. Weighted methods in noncommutative geometry.
    pdf