Vector bundles trivialized by proper morphisms and the fundamental group scheme
2010 ◽
Vol 10
(2)
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pp. 225-234
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Keyword(s):
AbstractLet X be a smooth projective variety defined over an algebraically closed field k. Nori constructed a category of vector bundles on X, called essentially finite vector bundles, which is reminiscent of the category of representations of the fundamental group (in characteristic zero). In fact, this category is equivalent to the category of representations of a pro-finite group scheme which controls all finite torsors. We show that essentially finite vector bundles coincide with those which become trivial after being pulled back by some proper and surjective morphism to X.
Keyword(s):
2013 ◽
Vol 15
(05)
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pp. 1350003
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2009 ◽
Vol 4
(2)
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pp. 209-221
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Keyword(s):
2014 ◽
Vol 22
(2)
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pp. 51-56
2017 ◽
Vol 166
(2)
◽
pp. 297-323
1994 ◽
Vol 80
(1)
◽
pp. 5-79
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2012 ◽
Vol 11
(4)
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pp. 835-854
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Keyword(s):