scholarly journals Néron’s pairing and relative algebraic equivalence

2012 ◽  
Vol 6 (7) ◽  
pp. 1315-1348 ◽  
Author(s):  
Cédric Pépin
Keyword(s):  
Algebraic Equivalence

scholarly journals Hochster’s theta pairing and algebraic equivalence

2011 ◽  
Vol 353 (2) ◽  
pp. 359-372 ◽  
Author(s):  
Olgur Celikbas ◽  
Mark E. Walker
Keyword(s):  
Algebraic Equivalence

scholarly journals Parameter Spaces for Algebraic Equivalence

2017 ◽  
Vol 2019 (6) ◽  
pp. 1863-1893 ◽  
Author(s):  
Jeffrey D Achter ◽  
Sebastian Casalaina-Martin ◽  
Charles Vial
Keyword(s):  
Abelian Varieties ◽  
Closed Field ◽  
Parameter Spaces ◽  
Algebraically Closed Field ◽  
Arbitrary Base ◽  
Closed Fields ◽  
Algebraic Equivalence ◽  
Integral Scheme ◽  
The Difference ◽  
Algebraically Closed Fields

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.

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