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The Tate Conjecture for Cubic Fourfolds over a Finite Field

Published online by Cambridge University Press:  04 December 2007

Norman Levin
Norman Levin
Affiliation:
IHES, 35 Route de Chartres, F91440 Bures-sur-Yvette, France. E-mail: [email protected]
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Abstract

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We prove the Tate conjecture for codimension 2 cycles on an ordinary cubic fourfold over a finite field. The proof involves the construction of canonical coordinates on the formal deformation space via a crystalline period map.

Keywords

Tate conjecturealgebraic cyclescanonical coordinatesperiod maps
Type
Research Article
Information
Compositio Mathematica , Volume 127 , Issue 1 , May 2001 , pp. 1 - 21
Copyright
© 2001 Kluwer Academic Publishers