arXiv subjects

Jinhyun Park

Publications and source records attributed to Jinhyun Park.

21 records · Page 2Linked to original sources

arXiv2008

A Hochschild-cyclic approach to additive higher Chow cycles

Over a field of characteristic zero, we introduce two motivic operations on additive higher Chow cycles: analogues of the Connes boundary $B$ operator and the shuffle product on Hochschild complexes. The former allows us to apply the formalism of mixed complexes to additive Chow complexes building a bridge between additive higher Chow theory and additive $K$-theory. The latter induces a wedge product on additive Chow groups for which we show that the Connes operator is a graded derivation for the wedge product using a variation of a Totaro's cycle. Hence, the additive higher Chow groups with the wedge product and the Connes operator form a commutative differential graded algebra. On zero-cycles, they induce the wedge product and the exterior derivation on the absolute Kähler differentials, answering a question of S. Bloch and H. Esnault.

math.AG↗

arXiv2007

Algebraic cycles and additive dilogarithm

For an algebraically closed field $k$ of characteristic 0, we give a cycle-theoretic description of the additive 4-term motivic exact sequence associated to the additive dilogarithm of J.-L. Cathelineau, that is the derivative of the Bloch-Wigner function, via the cubical additive higher Chow groups under one assumption. The 4-term functional equation of Cathelineau, an additive analogue of Abel's 5-term functional equation, is also discussed cycle-theoretically.

math.AG↗

arXiv2006

Algebraic cycles and Connes periodicity

We apply the classical technique on cyclic objects of Alain Connes to various objects, in particular to the higher Chow complex of S. Bloch to prove a Connes periodicity long exact sequence involving motivic cohomology groups. The Cyclic higher Chow groups and the Connes higher Chow groups of a variety are defined in the process and various properties of them are deduced from the known properties of the higher Chow groups. Applications include an equivalent reformulation of the Beilinson-Soulé vanishing conjecture for the motivic cohomology groups of a smooth variety $X$ and a reformulation of the conjecture of Soulé on the order of vanishing of the zeta function of an arithmetic variety.

math.AG↗