Research

 

Published/to appear:

  1. Some nontrivial examples of the BOS twisted spectral sequence (with Igor Kriz). New York J. Math. 22 (2016) 363–378. [Arxiv:1604] [NYJM].
  2. A primer to unstable motivic homotopy theory (with Benjamin Antieau). Surveys on Recent Developments in Algebraic Geometry, Proc. Sympos. Pure Math. 95 (2017), 305-370. [Arxiv:1605].
  3. On modules over motivic ring spectra (with Håkon Andreas Kolderup) Ann. K-Theory 5, 327-355 [Arxiv:1708.05651][AKT].
  4. Framed transfers and motivic fundamental classes (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 39 pages)  Journal of Topology. 13 (2020), 460-500. [Arxiv:1809] [JTop].
  5. Perfection in motivic homotopy theory. (with Adeel Khan, 10 pages). Proc. London. Math. Soc. 120 (2019), 28-38 [Arxiv:1812][PLMS].
  6. Modules over algebraic cobordism (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 40 pages) to appear in Forum. Math. Pi [Arxiv:1908] [ForumPi].
  7. Cdh descent, cdarc descent and Milnor excision (with Marc Hoyois, Ryomei Iwasa and Shane Kelly, 27 pages) to appear in Math. Annalen [Arxiv:2002] [Math. Ann.].
  8. THH and TC are (very) far from being homotopy functors (10 pages) to appear in JPAA [Arxiv:2007] [JPAA].

Preprints:

  1. Algebraic cobordism and étale cohomology (with Marc Levine, Markus Spitzweck and Paul Arne Østvær). [Arxiv:1711] (submitted and revised, comments welcome, last updated Feb 2019).
  2. Motivic infinite loop spaces (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson[Arxiv:1711] (submitted, last updated: April 2020). (slides)
  3. Thesis: Motivic contractibility of the space of rational maps (preliminary version, comments welcome, last updated April 2018) (To be split into two papers).
  4. Relative étale realizations of motivic spaces and Dwyer-Friedlander K-theory of noncommutative schemes. (with David Carchedi, 81 pages) [Arxiv:1810] (preliminary version, comments welcome, last updated October 2018).
  5.  On the infinite loop spaces of algebraic cobordism and the motivic sphere (with Tom Bachmann, Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 11 pages) [Arxiv:1911] (submitted, comments welcome, last updated March 2020).
  6. Voevodsky’s slice conjectures via Hilbert schemes (with Tom Bachmann, 8 pages) [Arxiv:1912] (submitted, comments welcome, last updated December 2019).
  7. Descent for semiorthogonal decompositions (with Benjamin Antieau, 30 pages) [Arxiv:1912] (submitted and revised, comments welcome, last updated November 7 2020).
  8. Scheiderer motives and equivariant higher topos theory (with Jay Shah, 78 pages). [Arxiv:1912] (submitted, comments welcome, last updated December 2019).
  9. Stable motivic invariants are eventually étale local  (with Tom Bachmann and Paul Arne Østvær, 32 pages) [Arxiv:2003] (submitted, comments welcome, last updated March 2020).
  10. Milnor excision for motivic spectra (with Marc Hoyois, Ryomei Iwasa and Shane Kelly, 9 pages) [Arxiv:2004(submitted, comments welcome, last updated, April 2020).
  11. A descent view on Mitchell’s theorem (with Denis Nardin and Lucy Yang, 5 pages) [Arxiv:2008] (submitted, comments welcome, last updated August 2020).
  12. Nilpotent extensions of \infty-categories and the cyclotomic trace (with Vladimir Sosnilo, 24 pages) [Arxiv:2010] (submitted, comments welcome, last updated October 2020).
  13. On Distributivity in Higher Algebra I: The Universal Property of Bispans (with Rune Haugseng, 77 pages) [Arxiv:2010] (preliminary version, comments welcome, last updated October 2020).
  14. Motivic colimits (with Tom Bachmann and Jeremiah Heller); a construction of motivic colimits with motivic power operations in view.

Mostly expository:

  1. Notes on motivic infinite loop space theory (with Tom Bachmann). [Arxiv:1912].
  2. Topological periodic cyclic homology of smooth \mathbb{F}_p-algebras. (After Bhatt-Morrow-Scholze) (MFO report, last updated May 2018).

In Preparation:

  1. Excision for Brauer stacks.
  2. Mod 2 Power operations on normed motivic spectra (with Tom Bachmann and Jeremiah Heller).
  3. K-theory of universal homeomorphisms (with Akhil Mathew and Jakub Witaszek). (slides) (video).
  4. On distributivity for higher algebra II (with Rune Haugseng).
  5. The Real integral Hodge conjecture for Chow-Witt groups (with Jay Shah).
  6.