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Proceedings of the London Mathematical Society Advance Access published online on October 27, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp039
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© 2009 London Mathematical Society

Formal completions of Néron models for algebraic tori

Oleg Demchenko

Department of Mathematics and Mechanics
St. Petersburg State University
Universitetskii pr. 28, Staryi Petergof
198504 St. Petersburg
Russia

Alexander Gurevich

Department of Mathematics
Bar-Ilan University
52900 Ramat-Gan
Israel
gurevia1@macs.biu.ac.il

Xavier Xarles

Departament de Matemàtiques
Universitat Autònoma de Barcelona
08193 Bellaterra
Barcelona
Catalonia
Spain
xarles@mat.uab.cat

Received 3 December 2008. Revision received 7 July 2009.

We calculate the formal group law that represents the completion of the Néron model for an algebraic torus over Q split in a tamely ramified abelian extension. To that end, we introduce an analogue of the fixed part of a formal group law with respect to a group action and give a method to compute its Honda p-types.

2000 Mathematics Subject Classification 14L05 (primary), 14G25, 11G35 (secondary).

The first author wishes to thank JSPS for financial support and the Mathematical Institute of Tohoku University for its hospitality. The second author was partially supported by the Minerva Foundation through the Emmy Noether Institute, the Ministry of Absorption, Israel, and the grant 3-3578 from the Ministry of Science, Israel, and the Russian Foundation for Basic Research. The third author was partially supported by the grant MTM 2006-11391 from DGI.


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