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Motivic invariants of algebraic tori


Author: Johannes Nicaise
Journal: Proc. Amer. Math. Soc. 139 (2011), 1163-1174
MSC (2000): Primary 14G10, 20G25, 14F20
DOI: https://doi.org/10.1090/S0002-9939-2010-10781-5
Published electronically: December 6, 2010
MathSciNet review: 2748411
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a trace formula and a global form of Denef and Loeser's motivic monodromy conjecture for tamely ramified algebraic tori over a discretely valued field. If the torus has purely additive reduction, the trace formula gives a cohomological interpretation for the number of components of the Néron model.


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Additional Information

Johannes Nicaise
Affiliation: Laboratoire Painlevé, Université Lille 1, CNRS - UMR 8524, Cité Scientifique, 59655 Villeneuve d’Ascq Cédex, France
Address at time of publication: Department of Mathematics, KULeuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium
Email: johannes.nicaise@wis.kuleuven.be

DOI: https://doi.org/10.1090/S0002-9939-2010-10781-5
Keywords: Motivic Serre invariant, trace formula, motivic zeta function, monodromy conjecture
Received by editor(s): April 14, 2009
Received by editor(s) in revised form: April 8, 2010
Published electronically: December 6, 2010
Additional Notes: The author was partially supported by ANR-06-BLAN-0183.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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