arXiv subjects

Tohru Kohrita

Publications and source records attributed to Tohru Kohrita.

4 recordsLinked to original sources

arXiv2024

Algebraic part of motivic cohomology with compact supports

Motivated by Murre's work on universal regular homomorphisms on Chow groups in codimension $2,$ we generalize the algebraic equivalence relation and regular homomorphisms to the context of Voevodsky motives over a field. In the Nisnevich topology, we prove the existence of \emph{universal} regular homomorphisms for a certain class of motivic cohomology groups, recovering Murre's theorem and the existence of Picard and Albanese varieties as special cases. This class also includes interesting cases such as higher Chow groups and Milnor $K$-groups. The appendix by Kahn proves that, for étale motives, universal regular homomorphisms exist for all geometric motives and compares them with those in the Nisnevich topology when both exist.

math.AG↗

arXiv2019

Filtrations on homotopy invariant sheaves with transfers

We construct filtrations on homotopy invariant sheaves with transfers and show that under Ayoub's conjectures on $n$-motives, our filtration agrees with the one conjectured by Ayoub and Barbieri-Viale if the latter exists. Our construction is directly motivated by the work of Pelaez.

math.AG↗

arXiv2017

On some negative motivic homology groups

For an arbitrary separated scheme $X$ of finite type over a finite field $\mathbb F_q$ and an integer $j=-1,-2,$ we prove under the assumption of resolution of singularities, that the two groups $H_{-1}(X,\mathbb Z(j))$ and $H_{-1}(π_0(X),\mathbb Z(j))$ are canonically isomorphic. This gives an explicit computation of $H_{-1}(X,\mathbb Z(j)).$

math.KT↗

arXiv2017

Deligne-Beilinson cycle maps for Lichtenbaum cohomology

We define Deligne-Beilinson cycle maps for Lichtenbaum cohomology $H_L^m(X, \mathbb Z(n))$ and that with compact supports $H_{c,L}^m(X, \mathbb Z(n))$ of an arbitrary complex algebraic variety $X.$ When $(m,n)=(2,1),$ the homological part of our cycle map with compact supports gives a generalization of the Abel-Jacobi theorem and its projection to the Betti cohomology yields that of the Lefschetz theorem on $(1,1)$-cycles for arbitrary complex algebraic varieties. In general degrees $(m,n),$ we show that the Deligne-Beilinson cycle maps are always surjective on torsion and have torsion-free cokernels. If $m \leq 2n,$ the version with compact supports induces an isomorphism on torsion, and so does the one without compact supports if $min \{2m-1, 2 \dim X+1 \} \leq 2n.$ We also characterize the algebraic part of Griffiths's intermediate Jacobians with a universal property.

math.AG↗