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Computing Néron–Severi groups and cycle class groups

Part of: Arithmetic problems. Diophantine geometry Cycles and subschemes (Co)homology theory

Published online by Cambridge University Press:  04 February 2015

Bjorn Poonen ,
Damiano Testa  and
Ronald van Luijk
Bjorn Poonen
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA email poonen@math.mit.edu
Damiano Testa
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK email adomani@gmail.com
Ronald van Luijk
Affiliation:
Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden, The Netherlands email rvl@math.leidenuniv.nl
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Abstract

Assuming the Tate conjecture and the computability of étale cohomology with finite coefficients, we give an algorithm that computes the Néron–Severi group of any smooth projective geometrically integral variety, and also the rank of the group of numerical equivalence classes of codimension $p$ cycles for any $p$.

Keywords

Néron–Severi groupscycle class groupsTate conjecture

MSC classification

Primary: 14C22: Picard groups
Secondary: 14C25: Algebraic cycles 14F20: Étale and other Grothendieck topologies and (co)homologies 14G25: Global ground fields 14G27: Other nonalgebraically closed ground fields

Information

Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 4 , April 2015 , pp. 713 - 734
Copyright
© The Author(s) 2015 

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