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. (Second) revised Draft (2019). to appear in Math. Zeitschrift (with a different title: A motivic homotopy theory without A^1-invariance). Online version.
- Laumon 1-motives and motives with modulus (with Shuji Saito). In preparation. Draft available on request (44 pages, 2018) (we currently stopped working on this project, and we plan to resume it as soon as the theory of Motives with Modulus is on solid ground).
- Rigidity for relative 0-cycles. (with Amalendu Krishna). arXiv:1802:00165v3[math.AG] (2018). Revised June. 2019. to appear in Ann. Sc. Norm. Sup. Pisa.
- Semi-purity for cycles with modulus (with Shuji Saito). arXiv:1812.01878 [math.AG] (2018). This paper is currently under revision.
- Bloch’s formula for 0-cycles with modulus and higher dimensional Class Field Theory (with Amalendu Krishna and Shuji Saito). arXiv:2002.01856 [math.AG] (2020).
- 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.