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Shafarevich Seminar
January 19, 2021 15:00, Moscow, online
 


On the integral Tate conjecture for 1-cycles on the product of a curve and a surface over a finite field

J.-L. Colliot-Thélène
Video records:
MP4 329.0 Mb
Supplementary materials:
Adobe PDF 248.2 Kb

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Abstract: Let $X$ be the product of a smooth projective curve $C$ and a smooth projective surface $S$ over a field $K$. Assume the Chow group of zero-cycles on $S$ is just $Z$ over any algebraically closed field extension of $F$ (example : Enriques surface). For $K$ the complex field, one may give counterexamples to the integral Hodge conjecture for 1-cycles (Benoist-Ottem) on $X$ and this may be understood from the point of view of unramified cohomology. For $K$ a finite field, in joint work with Federico Scavia (UBC, Vancouver) we give a simple condition on $C$ and $S$ which ensures that the integral Tate conjecture holds for 1-cycles on $X$. An equivalent formulation is a vanishing result for unramified cohomology of degree 3.

Supplementary materials: jlctmoscow19jan21revised.pdf (248.2 Kb)

Language: English
 
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