English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $f : X \rightarrow B$ be a proper flat dominant morphism between twosmooth quasi-projective complex varieties $X$ and $B$. Assume that there existsan integer $l$ such that all closed fibres $X_b$ of $f$ satisfy $CH_j(X_b) =\Q$ for all $j \leq l$. Then we prove an analogue of the projective bundleformula for $CH_i(X)$ for $i \leq l$. When $B$ is a surface, $X$ is projectiveand $l = \lfloor \frac{\dim X - 3}{2} \rfloor$, this makes it possible toconstruct a Chow-K\"unneth decomposition for $X$ that satisfies Murre'sconjectures. For instance we prove Murre's conjectures for complex smoothprojective varieties $X$ fibred over a surface (via a flat morphism) byquadrics, or by complete intersections of dimension 4 of bidegree $(2,2)$.

Chow groups of smooth varieties fibred by quadrics