Keywords: (algebraic) -theory and cobordism, motivic cohomology and algebraic cycles, (topological) cyclic homology in arithmetic geometry, cdh and valuation-theoretic methods in algebraic geometry, -algebraic geometry, Hilbert schemes and variants, abstract homotopy theory.
- Some nontrivial examples of the BOS twisted spectral sequence (with Igor Kriz). New York J. Math. 22 (2016) [Arxiv:1604] [NYJM].
- A primer to unstable motivic homotopy theory (with Benjamin Antieau). Surveys on Recent Developments in Algebraic Geometry, Proc. Sympos. Pure Math. 95 (2017) [Arxiv:1605].
- On modules over motivic ring spectra (with Håkon Andreas Kolderup) Ann. K-Theory. 5 (2020) [Arxiv:1708.05651][AKT].
- Framed transfers and motivic fundamental classes (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 39 pages) Journal of Topology. 13 (2020) [Arxiv:1809] [JTop].
- Perfection in motivic homotopy theory. (with Adeel Khan, 10 pages). Proc. London. Math. Soc. 120 (2019) [Arxiv:1812][PLMS].
- Modules over algebraic cobordism (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 40 pages) Forum Math. 8 (2020) [Arxiv:1908] [ForumPi].
- Cdh descent, cdarc descent and Milnor excision (with Marc Hoyois, Ryomei Iwasa and Shane Kelly, 27 pages) Math. Annalen. 379 (2021) [Arxiv:2002] [Math. Ann.].
- THH and TC are (very) far from being homotopy functors Journal of Pure and Applied Algebra, 225 (2021) [Arxiv:2007] [JPAA].
- Descent for semiorthogonal decompositions (with Benjamin Antieau) Adv. Math, 380 (2021) [Arxiv:1912] [AiM].
- Scheiderer motives and equivariant higher topos theory (with Jay Shah) Adv. Math. 382 (2021) [Arxiv:1912] [AiM].
- On the infinite loop spaces of algebraic cobordism and the motivic sphere (with Tom Bachmann, Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson) Épijournal Géom. Algébrique, Vol. 5. (2021) [Arxiv:1911] [EPIGA].
- On nilpotent extensions of -categories and the cyclotomic trace (with Vladimir Sosnilo) Int. Math. Res. Not., 14 (2021) [Arxiv:2010] [IMRN] (slides).
- Voevodsky’s slice conjectures via Hilbert schemes (with Tom Bachmann) [Arxiv:1912] to appear in Algebraic Geometry (Foundation Compositio) [Alg. Geom.].
- Algebraic cobordism and étale cohomology (with Marc Levine, Markus Spitzweck and Paul Arne Østvær) [Arxiv:1711] to appear in Geometry & Topology [G&T].
- Motivic infinite loop spaces (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson) [Arxiv:1711] to appear in Cambridge J. Math. [CJM] (slides).
- Milnor excision for motivic spectra (with Marc Hoyois, Ryomei Iwasa and Shane Kelly, 9 pages) [Arxiv:2004] to appear in J. reine angew. Math. (Crelle’s journal) [Crelle].
- Thesis: Motivic contractibility of the space of rational maps (preliminary version, comments welcome, last updated April 2018) (To be split into two papers).
- Relative étale realizations of motivic spaces and Dwyer-Friedlander -theory of noncommutative schemes. (with David Carchedi, 81 pages) [Arxiv:1810] (preliminary version, comments welcome, last updated October 2018).
- 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).
- A descent view on Mitchell’s theorem (with Denis Nardin and Lucy Yang, 5 pages) [Arxiv:2008] (submitted, comments welcome, last updated August 2020).
- On distributivity in higher algebra I: the universal property of bispans (with Rune Haugseng, 77 pages) [Arxiv:2010] (submitted, comments welcome, last updated January 2021).
- Motivic colimits and motivic extended powers (with Tom Bachmann and Jeremiah Heller, 32 pages) [Arxiv:2104] (preliminary version, comments welcome, last updated April 2021).
- -connected components of classifying spaces and purity for torsors (with Matthias Wendt and Girish Kulkarni, 22 pages) [Arxiv:2104] (submitted, comments welcome, last updated April 2021).
- Notes on motivic infinite loop space theory (with Tom Bachmann). [Arxiv:1912].
- Topological periodic cyclic homology of smooth -algebras. (After Bhatt-Morrow-Scholze) (MFO report, last updated May 2018).
- Mod 2 Power operations on normed motivic spectra (with Tom Bachmann and Jeremiah Heller).
- K-theory of universal homeomorphisms (with Akhil Mathew and Jakub Witaszek). (slides) (video).
- On distributivity for higher algebra II (with Rune Haugseng).
- The Real integral Hodge conjecture for Chow-Witt groups (with Jay Shah).
- Chow-Witt zero cycles of real schemes (with Aravind Asok)
Last updated: July 9 2021.