Geodesic
Invariants of upper motives
Documenta mathematica, Tome 18 (2013), pp. 1555-1572
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Let H be a homology theory for algebraic varieties over a field k. To a complete k-variety X, one naturally attaches an ideal HX​(k) 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.
DOI : 10.4171/dm/436
Classification : 14C25
Mots-clés : Grothendieck group, algebraic cobordism, upper motives, canonical dimension 
@article{10_4171_dm_436,
     author = {Olivier Haution},
     title = {Invariants of upper motives},
     journal = {Documenta mathematica},
     pages = {1555--1572},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/436},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/436/}
}
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Olivier Haution. Invariants of upper motives. Documenta mathematica, Tome 18 (2013), pp. 1555-1572. doi: 10.4171/dm/436

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