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]. Submitted (2017).
- Additive homotopy theory of schemes. Draft (2017). Part of this paper is the content of the second Chapter of my PhD Thesis.
- Laumon 1-motives and 1-motives with modulus (with Shuji Saito). In preparation.
- Motivic cohomology of normal crossing varieties and restriction of zero cycles. (with Amalendu Krishna). In preparation.
- Extensions of enriched Hodge structures and Jacobians with modulus. (with Stefan Müller-Stach and Thomas Weißschuh). In preparation.
Motives and algebraic cycles with moduli conditions. Ph.D. thesis, University of Duisburg-Essen (2016). DuEPublico ID: 41950. Available here.