Exterior Powers of Lubin-Tate Groups

S. Mohammad Hadi Hedayatzadeh

doi:10.5802/jtnb.895

S. Mohammad Hadi Hedayatzadeh ¹

¹ Department of Mathematics Mail Code 253-37 California Institute of Technology Pasadena, CA 91125, U.S.A.

Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 1, pp. 77-148.

Abstract
Résumé

Let $𝒪$ be the ring of integers of a non-Archimedean local field of characteristic zero and $π$ a fixed uniformizer of $𝒪$ . We prove that the exterior powers of a $π$ -divisible module of dimension at most 1 over a locally Noetherian scheme exist and commute with arbitrary base change. We calculate the height and dimension of the exterior powers in terms of the height of the given $π$ -divisible module. In the case of $p$ -divisible groups, the existence of the exterior powers are proved without any condition on the basis.

Soient $𝒪$ l’anneau des entiers d’un corps local non-archimédien de charactéristique zéro et $π$ une uniformisante de $𝒪$ . On démontre que les puissances extérieures d’un schéma en $𝒪$ -modules $π$ -divisible de dimension au plus 1 sur un schéma de base localement noetherian existent et commutent avec changements de base arbitraires. De même, on calcule la hauteur et la dimension des puissances extérieures en termes de la hauteur du groupe $p$ -divisible ou du schéma en $𝒪$ -modules $π$ -divisible donné. Dans le cas des groupes $p$ -divisibles, on démontre l’existence des puissances extérieures sans aucune hypothèse sur le schéma de base.

MR: 3346966

DOI: 10.5802/jtnb.895

Classification: 14L05, 14F30

Author's affiliations:

S. Mohammad Hadi Hedayatzadeh ¹

¹ Department of Mathematics Mail Code 253-37 California Institute of Technology Pasadena, CA 91125, U.S.A.

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     title = {Exterior {Powers} of {Lubin-Tate} {Groups}},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
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     year = {2015},
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S. Mohammad Hadi Hedayatzadeh. Exterior Powers of Lubin-Tate Groups. Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 1, pp. 77-148. doi : 10.5802/jtnb.895. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.895/

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