During my Ph.D. years I became interested in the theory of algebraic cycles and in its interaction with the theory of motives. In particular, I worked and I am working in the emerging area of non-homotopy invariant motives, a recent development of the theory of Vladimir Voevodsky that is based on insights of Spencer Bloch, Hélène Esnault, Bruno Kahn, Moritz Kerz, Shuji Saito and others.
Papers and Preprints:
- Algebraic cycles with moduli and regulator maps. (with Shuji Saito) arXiv:1412.0385 [math.AG]. Updated version (2017). Accepted for publication in J. of the Inst. of Math. Jussieu. First view.
- 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.
- 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.
- Torsion zero cycles with modulus on affine varieties. arXiv:1604.06294v2 [math.AG]. (2017). to appear in J. of Pure and App. Algebra. Online version.
- A cycle class map for zero cycles with modulus to higher relative K-groups. arXiv:1706.07126 [math.AG] (2017). Documenta Math, Volume 23, Pages 407-444, May 2018. Published version.
- Additive homotopy theory of schemes. Revised Draft (2018). Submitted.
- Laumon 1-motives and motives with modulus (with Shuji Saito). In preparation. Draft available on request (2018).
- Rigidity for relative 0-cycles. (with Amalendu Krishna). arXiv:1802:00165[math.AG] (2018). Revised Dec. 2018. Submitted.
- Semi-purity for cycles with modulus (with Shuji Saito). arXiv:1812.01878 [math.AG] (2018). Submitted.
- Levine-Weibel Chow group and motivic cohomology of singular varieties. (with Amalendu Krishna). In preparation.
- Rigidity for relative 0-cycles II. The quasi-projective case. (with Amalendu Krishna). In preparation.
- On the Levine-Weibel Chow group of product of curves (with Wataru Kai and Takao Yamazaki). In preparation.
Motives and algebraic cycles with moduli conditions. Ph.D. thesis, University of Duisburg-Essen (2016). DuEPublico ID: 41950. Available here.