Geodesic
Weak Lefschetz for Chow groups: Infinitesimal lifting
Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 65-84.

Voir la notice de l'article provenant de la source International Press of Boston

Let $X$ be a smooth projective variety over an algebraically closed field $k$ of characteristic zero, and let $Y \subset X$ be a smooth ample hyperplane section. The Weak Lefschetz conjecture for Chow groups states that the natural restriction map $\mathrm{CH}^p (X)_{\mathbb{Q}} \to \mathrm{CH}^p (Y)_{\mathbb{Q}}$ is an isomorphism for all $p \lt \dim (Y) / 2$. In this note, we revisit a strategy introduced by Grothendieck to attack this problem by using the Bloch-Quillen formula to factor this morphism through a continuous $\mathrm{K}$-cohomology group on the formal completion of $X$ along $Y$. This splits the conjecture into two smaller conjectures: one consisting of an algebraization problem and the other dealing with infinitesimal liftings of algebraic cycles. We give a complete proof of the infinitesimal part of the conjecture.
DOI : 10.4310/HHA.2014.v16.n2.a4
Classification : 14C25, 14C35
Keywords: $K$-theory, algebraic cycles 
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     title = {Weak {Lefschetz} for {Chow} groups: {Infinitesimal} lifting},
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D. Patel; G. V. Ravindra. Weak Lefschetz for Chow groups: Infinitesimal lifting. Homology, homotopy, and applications, Tome 16 (2014) no. 2, pp. 65-84. doi : 10.4310/HHA.2014.v16.n2.a4. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n2.a4/

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