ISSN:
1573-0514
Schlagwort(e):
Mathematics Subject Classification (1991): 14C25, 14C30.
;
Algebraic cycles
;
Deligne–Beilinson cohomology.
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
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(γ) 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.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1023/A:1007751500994
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