Formal completions of Néron models for algebraic tori

Oleg Demchenko; Alexander Gurevich; Xavier Xarles

doi:10.1112/plms/pdp039

Formal completions of Néron models for algebraic tori

Oleg Demchenko^*, Alexander Gurevich, Xavier Xarles

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	607-638
Number of pages	32
Journal	Proceedings of the London Mathematical Society
Volume	100
Issue number	3
DOIs	https://doi.org/10.1112/plms/pdp039
State	Published - May 2010
Externally published	Yes

Bibliographical note

Funding Information:
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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note = "Funding Information: 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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AU - Xarles, Xavier

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AB - 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.

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Formal completions of Néron models for algebraic tori

Abstract

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