On the numerical equivalence of algebraic cycles on potentially simple Abelian schemes of prime relative dimension

2005 ◽  
Vol 69 (1) ◽  
pp. 143-162 ◽  
Author(s):  
Sergei G Tankeev
Keyword(s):  
Algebraic Cycles ◽  
Relative Dimension ◽  
Numerical Equivalence ◽  
Abelian Schemes

scholarly journals Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Cristian González-Avilés
Keyword(s):  
Algebraic Cycles ◽  
Finitely Generated ◽  
Relative Dimension ◽  
Finiteness Theorems ◽  
Small Codimension

AbstractWe obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves over perfect fields. For example, if k is finitely generated over ℚ and X → C is a quadric fibration of odd relative dimension at least 11, then CH i(X) is finitely generated for i ≤ 4.

scholarly journals SOME NEW EXAMPLES OF SMASH-NILPOTENT ALGEBRAIC CYCLES

2017 ◽  
Vol 59 (3) ◽  
pp. 623-634 ◽  
Author(s):  
ROBERT LATERVEER
Keyword(s):  
Projective Variety ◽  
Smooth Projective Variety ◽  
Algebraic Cycles ◽  
Numerical Equivalence

AbstractVoevodsky has conjectured that numerical equivalence and smash-equivalence coincide for algebraic cycles on any smooth projective variety. Building on work of Vial and Kahn–Sebastian, we give some new examples of varieties where Voevodsky's conjecture is verified.

Apparent measure and relative dimension

2008 ◽  
Vol 42 (6-8) ◽  
pp. 733-746
Author(s):  
Fayçal Ben Adda
Keyword(s):  
Relative Dimension

An Elementary Proof of Suslin Reciprocity

2005 ◽  
Vol 48 (2) ◽  
pp. 221-236 ◽  
Author(s):  
Matt Kerr
Keyword(s):  
Elementary Proof ◽  
Function Fields ◽  
Algebraic Cycles ◽  
Important Special Case ◽  
Special Case

AbstractWe state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor K2-groups (for function fields) employed in the proof.

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