Preprints
On the logarithmic slice filtration Joint with F. Binda, D. Park.
Cousin complexes in motivic homotopy theory Joint with A. Druzhinin, H. Kolderup.
The integral motivic dual Steenrod algebra Joint with B. Dundas.
Logarithmic motivic homotopy theory Joint with F. Binda, D. Park.
The trivial fiber topology and framed motives over the integers Joint with A. Druzhinin, H. Kolderup.
The multiplicative structures on motivic homotopy groups Joint with D. Dugger, B. Dundas, D. Isaksen. To appear in Algebraic and Geometric Topology.
Punctured tubular neighborhoods and stable homotopy at infinity Joint with F. Déglise, A. Dubouloz.
Hochschild homology of mod-p motivic cohomology over algebraically closed fields Joint with B. Dundas, M. Hill, K. Ormsby. To appear in CAMS.
Milnor-Witt Motives Joint with T. Bachmann, B. Calmès, F. Déglise, J. Fasel. To appear in Memoirs of the AMS.
On etale motivic spectra and Voevodsky's convergence conjecture Joint with T. Bachmann, E. Elmanto. To appear in JEMS.
Publications
The second stable homotopy groups of motivic spheres Duke Math J. 173(6) (2024), 1017-1084. Joint with O. Röndigs, M. Spitzweck.
Bredon motivic cohomology of the complex numbers Documenta Mathematica, 29 (2024), 115-140. Joint with J. Heller, M. Voineagu.
Logarithmic prismatic cohomology via logarithmic THH IMRN, 22 (2023), 56 p. Joint with F. Binda, T. Lundemo, D. Park.
A Hochschild-Konstant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology Advances in Mathematics, 435, Part A (2023), 66 p. Joint with F. Binda, T. Lundemo, D. Park.
Geometric models for algebraic suspensions IMRN, 20 (2023), 34 p. Joint with A. Asok, A. Dubouloz.
Framed motivic Γ-spaces Izvvestiya Math., 87 (2023), 3-32. Joint with G. Garkusha, I. Panin.
Triangulated categories of logarithmic motives over a field Astérisque, 433 (2022), 280 p. Joint with F. Binda, D. Park.
Motives and homotopy theory in logarithmic geometry Comptes Rendus. Mathématique, 360 (2022), 717-727. Joint with F. Binda, D. Park.
Algebraic cobordism and etale cohomology Geometry and Topology, 26 (2022), 477-585. Joint with E. Elmanto, M. Levine, M. Spitzweck.
Topological models for stable motivic invariants of regular number rings Forum of Mathematics, Sigma, 10 (2022), 27 p. Joint with T. Bachmann.
A1-homotopy theory and contractible varieties: a survey In: Homotopy Theory and Arithmetic Geometry - Motives and Diophantine Aspects, LMS-CMI Research School London. Springer-Verlag. Lecture Notes in Mathematics, no. 2292 (2021), 145-212. Joint with A. Asok.
On functorial (co)localization of algebras and modules over operads Abh. Math. Semin. Univ. Hamburg, 91 (2021), 153-178. Joint with J. J. Gutiérrez, O. Röndigs, M. Spitzweck.
Motivic stable homotopy groups In Handbook of Homotopy Theory. CRC Press/Chapman and Hall Handbooks in Mathematics Series (2020) 35 p. Joint with D. Isaksen.
Hermitian K-theory, Dedekind ζ-functions, and quadratic forms over rings of integers in number fields Cambridge Journal of Mathematics, 8 (2020), 505-607. Joint with J. I. Kylling, O. Röndigs.
On very effective hermitian K-theory Mathematische Zeitschrift, 294 (2020), 1021-1034. Joint with A. Ananyevskiy, O. Röndigs.
A1-contractibility of affine modifications International Journal of Mathematics, 30 (2019), No. 14, 1950069. Joint with A. Dobouloz, S. Pauli.
The first stable homotopy groups of motivic spheres Annals of Mathematics, 189 (2019), 1-74. Joint with O. Röndigs, M. Spitzweck.
Topological comparison theorems for Bredon motivic cohomology Transactions of the American Mathematical Society, 371 (2019), 2875-2921. Joint with J. Heller, M. Voineagu.
Cellularity of hermitian K-theory and Witt-theory In K-Theory - Proceedings of the International Colloquium, Mumbai, 2016. Hindustan Book Agency (2018), 35-40. Joint with O. Röndigs, M. Spitzweck.
The motivic Hopf map solves the homotopy limit problem for K-theory Documenta Mathematica, 23 (2018), 1405-1424. Joint with O. Röndigs, M. Spitzweck.
Rigidity for equivariant pseudo pretheories Journal of Algebra, 516 (2018), 373-395. Joint with J. Heller, C. Ravi.
Vanishing in stable motivic homotopy sheaves Forum of Mathematics, Sigma, 6 (2018). Joint with K. Ormsby, O. Röndigs.
The motivic Steenrod algebra in positive characteristic Journal of the European Mathematical Society, 19 (2017), 3813-3849. Joint with M. Hoyois, S. Kelly.
Two-complete stable motivic stems over finite fields Algebraic and Geometric Topology, 17 (2017), 1059-1104. Joint with G. Wilson.
A1-contractibility of Koras-Russell threefolds Algebraic Geometry, 3 (2016), 407-423. Joint with M. Hoyois, A. Krishna.
The multiplicative structure on the graded slices of hermitian K-theory and Witt-theory Homology, Homotopy and Applications, 18 (2016), 373-380. Joint with O. Röndigs.
Slices of hermitian K–theory and Milnor’s conjecture on quadratic forms Geometry and Topology, 20 (2016), 1157-1212. Joint with O. Röndigs.
Motivic homotopy theory of group scheme actions Journal of Topology, 8 (2015), 1202-1236. Joint with J. Heller, A. Krishna.
Equivariant cycles and cancellation for motivic cohomology Documenta Mathematica, 20 (2015), 269-332. Joint with J. Heller, M. Voineagu.
Existence and uniqueness of E∞ structures on motivic K-theory spectra Journal of Homotopy and Related Structures (JHRS), 10 (2015), 333-346. Joint with N. Naumann, M. Spitzweck.
The homotopy fixed point theorem and the Quillen–Lichtenbaum conjecture in hermitian K-theory Advances in Mathematics, 278 (2015), 34-55. Joint with J. Berrick, M. Karoubi, M. Schlichting.
Stable motivic π1 of low-dimensional fields Advances in Mathematics, 265 (2014), 97- 131. Joint with K. Ormsby.
K-theory and mapping spaces: an appendix to Equivariant semi-topological K-homology and a theorem of Thomason Journal of K-Theory, 13 (2014), 1-8.
Hermitian periodicity and cohomology of infinite orthogonal groups Journal of K-Theory, 12 (2013), 203-211. Joint with A. J. Berrick, M. Karoubi.
Motivic Brown-Peterson invariants of the rationals Geometry and Topology, 17 (2013), 1671-1706. Joint with K. Ormsby.
Motivic slices and coloured operads Journal of Topology, 5 (2012), 727- 755. Joint with J. J. Gutierrez, O. Röndigs, M. Spitzweck.
Nisnevich descent for K-theory of Deligne-Mumford stacks Journal of K-Theory, 9 (2012), 291-331. Joint with A. Krishna.
Motivic twisted K-theory Algebraic and Geometric Topology, 12 (2012), 565-599. Joint with M. Spitzweck.
Periodicity of hermitian K-groups Journal of K-Theory, 7 (2011), 429-493. Joint with A. J. Berrick, M. Karoubi.
Erratum to: Rigidity in motivic homotopy theory Mathematische Annalen, 350 (2011), 755-756. Joint with O. Röndigs.
Hermitian K-theory and 2-regularity for totally real number fields Mathematische Annalen, 349 (2011), 117-159. Joint with A. J. Berrick, M. Karoubi.
Universality of mod-p cohomology Topology and its Applications, 157 (2010), 2864-2872. Joint with M. Spitzweck.
Homotopy theory of cyclic presheaves Mathematica Scandinavica, 107 (2010), 30-42. Joint with S. Seteklev.
Motivic strict ring models for K-theory Proceedings of the American Mathematical Society, 138 (2010), 3509-3520. Joint with O. Röndigs, M. Spitzweck.
A Bott inverted model for equivariant unitary topological K-theory Mathematica Scandinavica, 106 (2010), 211-216. Joint with M. Spitzweck.
Rigidity for equivariant K-theory C. R. Math. Acad. Sci. Paris, 347 (2009), 1403-1407. Joint with S. Yagunov.
Motivic Landweber Exactness Documenta Mathematica, 14, 551-593. Joint with N. Naumann, M. Spitzweck.
Chern classes, K-theory and Landweber exactness over nonregular base schemes Fields Institute Communications, 56 (2009), 307-317. Joint with N. Naumann, M. Spitzweck.
The Bott inverted infinite projective space is homotopy algebraic K-theory Bull. London Math, Soc. 41 (2009), 281-292. Joint with M. Spitzweck.
Modules over motivic cohomology Advances in Mathematics, 219 (2008), 689-727. Joint with O. Röndigs.
Rigidity in motivic homotopy theory Mathematische Annalen, 341 (2008), 651-675. Joint with O. Röndigs.
Voevodsky’s Nordfjordeid Lectures: Motivic Homotopy Theory Universitext Series in Mathematics, Springer-Verlag (2007), 147-220. Joint with O. Röndigs, V. Voevodsky.
Rigidity for pseudo pretheories Inventiones Math., 166 (2006), 95-102. Joint with A. Rosenschon.
Motives and modules over motivic cohomology C. R. Math. Acad. Sci Paris, 342 (2006), 751-754. Joint with O. Röndigs.
Descent for K-theories J. Pure Appl. Algebra, 206 (2006), 141-152. Joint with A. Rosenschon.
The homotopy limit problem for two-primary algebraic K-theory Topology, 44 (2005), 1159-1179. Joint with A. Rosenschon.
K-theory of surfaces at the prime 2 K-Theory, 33 (2005), 215-250. Joint with A. Rosenschon.
On A(X) → TC(X) for some X K-Theory, 31 (2004), 345-355.
Wild kernels at the prime 2 Acta Arithmetica, 112 (2004), 109-130.
The homotopy type of two-regular K-theory Progress in Mathematics, 215, 167-178 (2004). Joint with L. Hodgkin.
Motivic functors Documenta Mathematica, 8 (2003), 489-525. Joint with B. I. Dundas, O. Röndigs.
Enriched functors and stable homotopy theory Documenta Mathematica, 8 (2003), 409-488. Joint with B. I. Dundas, O. Röndigs.
K-groups with finite coefficients and arithmetic Mathematica Scandinavica, 91 (2003), 41-52.
A norm principle in higher algebraic K-theory Bull. London Math. Soc. 35 (2003), 491-498.
K-theory of curves over number fields J. Pure Appl. Algebra, 178 (2003), 307-333. Joint with A. Rosenschon.
Étale descent for real number fields Topology, 42 (2003), 197-225.
Periodicity in K-groups of certain fields Rendiconti del Seminario Matematico, 107 (2002), 1-8.
Algebraic K-theory spectra of non-exceptional two-regular number fields Contemp. Math. Amer. Math. Soc., 265 (2000), 187-192.
Two-primary algebraic K-theory of two-regular number fields Math. Z., 233 (2000), 251-263. Joint with J. Rognes.
On the Coates-Sinnott conjecture K-Theory, 19 (2000), 195-209. Joint with P. Cornacchia.
Calculations of two-primary K-theory of some group rings K-Theory, 16 (1999), 391-397.
On 2-primary algebraic K-theory of quadratic number rings with focus on K_2 Acta Arithmetica, LXXXVII.3 (1999), 223-243. Joint with M. Crainic.
Lecture notes
Hermitian K-groups and motives Princeton University seminar, 2024.
Motives of logarithmic schemes LMU seminar, 2022.
Summer school on Motives and Artithmetic groups Motives and hermitian K-theory of number rings, IRMA, Strasbourg, 2022.
Motivic homotopy types of algebraic varieties Topics in Motivic Homotopy Theory, 2021.
Motivic homotopy theory at infinity eCHT Research Seminar, 2020.
Stable motivic invariants are eventually etale local University of Zurich, 2019.
Seminar talk on motivic homotopy theory Radbound Excellence Initiative, 2019.
Summer school on motives and stacks Equivariant motivic homotopy theory, University of Duisburg-Essen, 2019.
Talk on framed motivic Gamma-spaces. Ivan Panin 60th birthday conference Euler Institute, St. Petersburg, 2019.
Musings on Hermitian K-theory; New Trends in K-theory and Homotopy Theory, Max Karoubi's 80th birthday Institute Henri Poincaré, Paris, 2018.
Talk at Euler International Mathematical Institute in St. Petersburg Euler Institute, St. Petersburg, 2018.
Motivic homotopies. University of Duisburg-Essen, 2014.
Books
Homotopy type of C*-algebras Frontiers in Mathematics, Springer-Verlag, 2010.
Motivic homotopy theory Universitext Series in Mathematics, Springer-Verlag, 2007. Joint with B. I. Dundas, M. Levine, O. Röndigs, V. Voevodsky.
Algebraic Topology The Abel Symposium 2007. Editors: N. Baas, E. M. Friedlander, B. Jahren, P. A. Østvær.
Video
Motivic homotopy types at infinity electronic Computational Homotopy Theory (eCHT), 2020.
Hva er motivisk geometri? Centre for Advanced Study, 2020.
A^1 contractible varieties Hausdorff Center for Mathematics, Bonn, 2017.
The motivic Hopf map and the homotopy limit problem for hermitian K theory Hausdorff Center for Mathematics, Bonn, 2016.