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].
  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). to appear in Comptes Rendus Mathématique. (11 pages, revised May 2022).

Preprints (intended for publication):

  1. On the cohomology of reciprocity sheaves (with Kay Rülling and Shuji Saito). arXiv:2010.03301 [math.AG] (116 pages, 2020). Submitted.
  2. Derived log Albanese sheaves (with Alberto Merici and Shuji Saito). arXiv:2107.00984 [math.AG] (57 pages, 2021). Submitted.
  3. GAGA problems for the Brauer group via derived geometry (with Mauro Porta). arXiv:210703914 [math.AG] (33 pages, 2021). Submitted.
  4. Suslin homology via cycles with modulus and applications (with Amalendu Krishna). arXiv:2202.06808 [math.AG] (27 pages, 2022).

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 MathematicsAmerican 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.