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We show that the additive higher Chow groups of regular schemes over a field induce a Zariski sheaf of pro-differential graded algebras, the Milnor range of which is isomorphic to the Zariski sheaf of big de Rham–Witt complexes. This provides an explicit cycle-theoretic description of the big de Rham–Witt sheaves. Several applications are derived.
Based on the algebraic cobordism theory of Levine and Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence.
We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the semi-topological K0-groups. We also show that with finite coefficients, this theory agrees with the algebraic cobordism theory.
We compute our cobordism theory for some low dimensional varieties. The results on infinite generation of some Griffiths groups by Clemens and on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms of this cobordism theory.
Inflammatory bowel diseases (IBD) are chronically relapsing inflammatory disorders of the intestine. Although some therapeutic agents, including steroids, are available for the treatment of IBD, these agents have limited use. Therefore, dietary supplements have emerged as possible interventions for IBD. Japanese honeysuckle flower, the flower of Lonicera japonica, is a well-known dietary supplement and has been used to prevent or treat various inflammatory diseases. In the present study, we investigated the effects of L. japonica on experimental murine colitis. Colitis was induced by 5 % dextran sulphate sodium (DSS) in Balb/c mice. The water extract of L. japonica (LJE) at doses of 20, 100 or 500 mg/kg was orally administered to mice twice per day for 7 d. Body weight, colon length and a histological damage score were assessed to determine the effects on colitis. Cytokine profiles were assessed to examine the effects on helper T (Th) cell-related immunological responses. In addition, CD4+CD25+Foxp3+T cells were analysed in vivo and in vitro for investigating the effects on regulatory T (Treg) cells. LJE showed dose-dependent inhibitory effects against colon shortening, weight loss and histological damage. LJE down-regulated IL-1β, TNF-α, interferon-γ, IL-6, IL-12 and IL-17. However, LJE did not show any significant effects on IL-10, IL-23, transforming growth factor-β1 and Treg cell populations. In conclusion, LJE showed protective effects against DSS-induced colitis via the Th1/Th17 pathway and not via Treg cell-related mechanisms.
For a perfect field k, we use the techniques of Bondal-Kapranov and Hanamura to construct a tensor triangulated category of mixed motives over the truncated polynomial ring k[t]/(tm+1). The extension groups in this category are given by Bloch's higher Chow groups and the additive higher Chow groups. The main new ingredient is the moving lemma for additive higher Chow groups by the authors and its refinements.
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