Mathematics

Research interest: Arithmetic and algebraic geometry. In particular: cycles and algebraic K-theory, derived algebraic geometry, motivic homotopy theory.

Papers:

  1. Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus (with Jin Cao, Wataru Kai and Rin Sugiyama) J. of Algebra, Volume 469, 1 January 2017, Pages 437–463. Preprint version arXiv:1503.02161 [math.AG]. Published version.
  2. Zero cycles with modulus and zero cycles on singular varieties. (with Amalendu Krishna)  Compositio Math., Volume 154, 1, January 2018, Pages 120-187. Preprint version arXiv:1512.04847 [math.AG]. Published version.
  3. Torsion zero cycles with modulus on affine varieties. J. of Pure and App. Algebra, Volume 222, Issue 1, January 2018, Pages 61-74. Preprint version arXiv:1604.06294v2 [math.AG]. Published version.
  4. A cycle class map for zero cycles with modulus to higher relative K-groups. Documenta Math, Volume 23, Pages 407-444, May 2018. Preprint version arXiv:1706.07126 [math.AG] (2017). Published version.
  5. Algebraic cycles with moduli and regulator maps. (with Shuji Saito)  J. of the Inst. of Math. Jussieu, Volume 18, Issue 6, November 2019, Pages 1233-1293. Preprint version arXiv:1412.0385 [math.AG]. Published version.
  6. A motivic homotopy theory without A^1-invariance. Math. Zeitschrift, Volume 295, pages 1475–1519(2020). Preprint version arXiv:1910.01339 [math.AG]. Published version.
  7. Rigidity for relative 0-cycles. (with Amalendu Krishna). Ann. Sc. Norm. Sup. Pisa Cl. Sci. (5) Vol. XXII (2021), 241-267. Preprint version arXiv:1802:00165v3 [math.AG]. Published version.
  8. Connectivity and purity for logarithmic motives (with Alberto Merici). to appear in J. of the Inst. Math. Jussieu. Preprint version arXiv:2012.08361 [math.AG] (42 pages, revised May 2021). Published version. (A small Erratum is available: the ArXiv version is updated accordingly).
  9. Bloch’s formula for 0-cycles with modulus and higher dimensional Class Field Theory (with Amalendu Krishna and Shuji Saito). to appear in J. of Algebraic Geom. Preprint version arXiv:2002.01856 [math.AG] (46 pages, revised August 2021).
  10. Triangulated categories of logarithmic motives over a field. (with Doosung Park and Paul Arne Østvaer). Astérisque. Tome 433, pp. 280, (2022). Preprint version arXiv:2004.12298 [math.AG]. Published version.
  11. Zero cycle groups on algebraic varieties (with Amalendu Krishna). J. de l’École Polytechnique – Mathématiques. Vol. 9 (2022), pp. 281-325. Preprint version arXiv:2104.07968 [math.AG]. Published version. 
  12. Motives and homotopy theory in logarithmic geometry. (with Doosung Park and Paul Arne Østvaer). Comptes Rendus Mathématique. Volume 360 (2022), pp. 717-727. Published version.
  13. On the cohomology of reciprocity sheaves (with Kay Rülling and Shuji Saito). Forum of Mathematics, Sigma, 10, E72. doi:10.1017/fms.2022.51 (2022). Preprint version arXiv:2010.03301 [math.AG]. Published version.
  14. Suslin homology via cycles with modulus and applications (with Amalendu Krishna). Transactions of the AMS. Volume 376, Number 2, (February 2023), pp. 1445–1473. Preprint version arXiv:2202.06808 [math.AG]. Published version.
  15. Derived log Albanese sheaves (with Alberto Merici and Shuji Saito). Advances in Math. Volume 417 (2023). Preprint version arXiv:2107.00984 [math.AG]. Published version.

Preprints (intended for publication):

  1. Descent problems for derived Azumaya algebras (with Mauro Porta). arXiv:210703914 [math.AG] (33 pages, Major revision 2023). Submitted. (The old title of the paper was: GAGA problems for the Brauer group via derived geometry).
  2. On the p-adic weight-monodromy conjecture for complete intersetions in toric varieties (with Hiroki Kato and Alberto Vezzani). arXiv:2207.00369 [math.AG] (35 pages, 2022). Submitted.
  3. A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology (with Tommy Lundemo, Doosung Park and Paul Arne Østvaer). arXiv:2209.14182 [math.AG] (44 pages, 2022). Submitted.
  4. Logarithmic motivic homotopy theory (with Doosung Park and Paul Arne Østvaer). (177 pages, March 2023). Very(!) preliminary version, subject to change! Comments welcome. arXiv:2303.02729 [math.AG].

Editorial work:

Motivic homotopy theory and refined enumerative geometry. Proceedings of the Conference MREG at the University of Duisburg-Essen in 2018. Volume 745 of Contemporary Mathematics, American Mathematical Society. F. Binda, M. Levine, M. T. Nguyen, O. Röndigs editors. April 2020

Thesis:

Motives and algebraic cycles with moduli conditions. Ph.D. thesis, University of Duisburg-Essen (2016). DuEPublico ID: 41950. Available here.