Searcharxiv⌕ Search

arXiv subjects

Kenichiro Kimura

Publications and source records attributed to Kenichiro Kimura.

13 recordsLinked to original sources
arXiv2026

On a relation of a conjecture of Goncharov to the co-Lie algebra of Bloch-Kriz mixed Tate motives

Goncharov defined for each field $F$ and an integer $n$ greater than 1 a certain group $B_n(F)$. We consider the possibility of defining a linear map from $B_n(F)$ to the co-Lie algebra of the category of mixed Tate motives defined by Bloch and Kriz, in terms of motivic polylogarithms. We give results which support this possibility assuming part of the conjecture by Beilinson and Soulé on vanishing of $K$-groups of fields.

math.AG↗
arXiv2024

An application of a Hodge realization of Bloch-Kriz mixed Tate motives

Beilinson and Deligne proved a weak version of Zagier's conjucture on special values of Dedekind zeta functions assuming the existence of a category of mixed Tate motives which has certain properties. We show that Bloch-Kriz category of mixed Tate motives together with a Hodge realization which we constructed has the required properties.

math.NT↗
arXiv2020

Semi-algebraic chains on projective varieties and the Abel-Jacobi map for higher Chow cycles

We will show that the singular cohomology groups of a smooth quasi-projective complex variety relative to a normal crossing divisor can be described in terms of delta-admissible chains. Roughly speaking, a delta-admissible chain is a simplicial semi-algebraic chain meeting the "faces" properly. As an application, we show that the Abel-Jacobi map for higher Chow cycles can be described via delta-admissible chains. As an example, we will describe the Hodge realization of the polylog cycles constructed by Bloch-Kriz in terms of the Abel-Jacobi map.

math.AG↗
arXiv2015

Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula, Part I: convergence theorems

In this paper consisting of two parts, we study the integral of a logarithmic differential form on a compact semi-algebraic set in R^n or C^n. In Part I, we prove the convergence of the integral when the semi-algebraic set satisfies allowability (or admissibility), a condition on the dimension of the intersection of the set and the pole divisor of the differential form.

math.AG↗
arXiv2010

Relative DGA and mixed elliptic motives

Bloch and Kriz construct an abelian category of mixed Tate motives as the category of comodules over a Hopf algebra obtained by the bar construction of the DGA of cycle complexes. In this paper we generalize their construction to give the definition of a category of mixed elliptic motives, i.e. a Tannakian category of mixed motives generated by an elliptic curve. We introduce the notion of a relative DGA over a reductive group. Then the category of mixed elliptic motives is defined as the category of comodules over the relative bar construction of a certain DGA $A_{EM}$ which is constructed from cycle complexes. The elliptic polylogarithm of Beilinson-Levin gives an interesting object in this category.

math.AG↗
arXiv2006

Nori's construction and the second Abel-Jacobi map

The first purpose of this note is to give a partial exposition of the $l$-adic realization of Nori's category of motives. The second one is to give a simple description of the second $l$-adic Abel-Jacobi map.

math.AG↗
arXiv2005

Murre's conjectures for certain product varieties

We consider Murre's conjectures on Chow groups for a fourfold which is a product of two curves and a surface. We give a result which concerns Conjecture D:the kernel of a certain projector is equal to the homologically trivial part of the Chow group. We also give a proof of Conjecture B for a product of two surfaces.

math.AG↗
arXiv2004

Zero-cycles on self-product of modular curves

We use the elements in $K$-cohomology groups which are constructed by Flach and Mildenhall to obtain a finiteness result for the torsion part of the Chow group of a self-product of a modular curve.

math.AG↗
arXiv2002

Elliptic units in $K_2$

We present certain norm-compatible systems in $K_2$ of function fields of some CM elliptic curves. We demonstrate that these systems have some properties similar to elliptic units.

math.AG↗
arXiv2002

On $K_1$ of a self-product of a curve

We present elements of $H^1(C\ti C, K_2)$ for certain specific curves C.The image of the element under the boundary map arising from the localization sequence of K-theory is the graph of frobenius endomorphism of the reduction of the curve modulo 3.

math.AG↗
arXiv2000

Euler systems of K_2 of CM elliptic curves

We construct certain systems of elements in K_2 of CM elliptic curves. When the classnumber of the field of CM is 1, the image of this system under the regulator map forms an Euler system in the sense of Rubin.

math.AG↗