Mathematics

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:

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. A cycle class map for zero cycles with modulus to higher relative K-groups. arXiv:1706.07126 [math.AG]. Submitted (2017).
  6. Additive homotopy theory of schemes.  Draft (2017).  Part of this paper is the content of the second Chapter of my PhD Thesis.
  7.  Laumon 1-motives and 1-motives with modulus (with Shuji Saito). In preparation.
  8. Motivic cohomology of normal crossing varieties and restriction of zero cycles. (with Amalendu Krishna). In preparation. 
  9. Extensions of enriched Hodge structures and Jacobians with modulus. (with Stefan Müller-Stach and Thomas Weißschuh). In preparation. 

Thesis:

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