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

Cristian González-Avilés

doi:10.2478/s11533-009-0043-2

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

Open Mathematics ◽

10.2478/s11533-009-0043-2 ◽

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.

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Equivalence relations on algebraic cycles and subvarieties of small codimension

Algebraic Geometry–Arcata 1974 - Proceedings of Symposia in Pure Mathematics ◽

10.1090/pspum/029/0369359 ◽

1975 ◽

pp. 129-164 ◽

Cited By ~ 16

Author(s):

Robin Hartshorne

Keyword(s):

Algebraic Cycles ◽

Equivalence Relations ◽

Small Codimension

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

Izvestiya Mathematics ◽

10.1070/im2005v069n01abeh000525 ◽

2005 ◽

Vol 69 (1) ◽

pp. 143-162 ◽

Cited By ~ 5

Author(s):

Sergei G Tankeev

Keyword(s):

Algebraic Cycles ◽

Relative Dimension ◽

Numerical Equivalence ◽

Abelian Schemes

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Algebraic Cycles and Motives

10.1017/cbo9780511721496 ◽

2007 ◽

Keyword(s):

Algebraic Cycles

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Lectures on Algebraic Cycles

10.1017/cbo9780511760693 ◽

2009 ◽

Cited By ~ 14

Author(s):

Spencer Bloch

Keyword(s):

Algebraic Cycles

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Automorphisms of finite order of nilpotent groups II

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.51.2014.4.1297 ◽

2014 ◽

Vol 51 (4) ◽

pp. 547-555 ◽

Cited By ~ 1

Author(s):

B. Wehrfritz

Keyword(s):

Nilpotent Group ◽

Finite Order ◽

Finite Index ◽

Nilpotent Groups ◽

Finitely Generated

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

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