Geodesic
Invariants of upper motives
Documenta mathematica, Tome 18 (2013), pp. 1555-1572.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $H$ be a homology theory for algebraic varieties over a field $k$. To a complete $k$-variety $X$, one naturally attaches an ideal $\MH{X}$ of the coefficient ring $H(k)$. We show that, when $X$ is regular, this ideal depends only on the upper Chow motive of $X$. This generalises the classical results asserting that this ideal is a birational invariant of smooth varieties for particular choices of $H$, such as the Chow group. When $H$ is the Grothendieck group of coherent sheaves, we obtain a lower bound on the canonical dimension of varieties. When $H$ is the algebraic cobordism, we give a new proof of a theorem of Levine and Morel. Finally we discuss some splitting properties of geometrically unirational field extensions of small transcendence degree.
Classification : 14C25
Keywords: upper motives, canonical dimension, Grothendieck group, algebraic cobordism 
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     author = {Haution, Olivier},
     title = {Invariants of upper motives},
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     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a2/}
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Haution, Olivier. Invariants of upper motives. Documenta mathematica, Tome 18 (2013), pp. 1555-1572. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a2/