Parameter Spaces for Algebraic Equivalence
2017 ◽
Vol 2019
(6)
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pp. 1863-1893
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Keyword(s):
Abstract A cycle is algebraically trivial if it can be exhibited as the difference of two fibers in a family of cycles parameterized by a smooth integral scheme. Over an algebraically closed field, it is a result of Weil that it suffices to consider families of cycles parameterized by curves, or by abelian varieties. In this article, we extend these results to arbitrary base fields. The strengthening of these results turns out to be a key step in our work elsewhere extending Murre’s results on algebraic representatives for varieties over algebraically closed fields to arbitrary perfect fields.
1980 ◽
Vol 29
(4)
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pp. 462-468
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2010 ◽
Vol 7
(1)
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pp. 55-89
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2018 ◽
Vol 71
(4)
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pp. 819-842
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1981 ◽
Vol 31
(2)
◽
pp. 136-141
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Keyword(s):
1985 ◽
Vol 38
(3)
◽
pp. 330-350
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2004 ◽
Vol 77
(1)
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pp. 123-128
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