Indecomposable Elements in K1 of a Smooth Projective Variety期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Indecomposable Elements in K1 of a Smooth Projective Variety

Authors:	Andreas Rosenschon

Institution:	(1) Department of Mathematics, University of Maryland, College Park, MD, 20742, U.S.A.

Abstract:	Let X be a smooth projective variety over the complex numbers. We consider the cohomology of the sheaves ${\mathcal{H}}_{\mathcal{D}}^q \left( {{\mathbb{Z}}\left( r \right)} \right)$ and ${\mathcal{H}}^q \left( {\mathbb{C}} \right)/{\mathcal{F}}^r {\mathcal{H}}^q$ arising from Deligne–Beilinson cohomology and the Hodge filtration on the singular cohomology of X. We show that one can identify $H^1 \left( {X,{\mathcal{F}}_{^{\mathbb{Z}} }^{22} } \right)$ with the image of the truncated regulator map c¯2,1. In particular, this implies that $H^1 \left( {X,{\mathcal{F}}_{^{\mathbb{Z}} }^{22} } \right)$ is countable. Since this group is a direct summand of coker $\left\{ {\gamma {\text{:Pic}}\left( X \right) \otimes {\mathbb{C}}^* \to H^1 \left( {X,{\mathcal{K}}_2 } \right)} \right\}$ , this gives a partial answer to Voisin's conjecture that cocker() is countable. In the case of X a surface, we prove that the Albanese kernel T(X) is isomorphic to the group of global sections of ${\mathcal{H}}_{\mathcal{D}}^3 \left( {{\mathbb{Z}}\left( 2 \right)} \right)$ if and only if pg=0.

Keywords:	Mathematics Subject Classification (1991): 14C25 14C30 Algebraic cycles Deligne– Beilinson cohomology
本文献已被 SpringerLink 等数据库收录！