$p$-adic non-commutative analytic subgroup theorem

Duc Hiep Pham

doi:10.5802/crmath.325

Théorie des nombres

p

-adic non-commutative analytic subgroup theorem

Duc Hiep Pham ¹

¹ University of Education, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 933-936.

Résumé

In this paper, we formulate and prove the so-called $p$ -adic non-commutative analytic subgroup theorem. This result is seen as the $p$ -adic analogue of a recent theorem given by Yafaev in [11].

Reçu le : 2021-07-15
Révisé le : 2021-09-20
Accepté le : 2022-01-10
Publié le : 2022-09-14

DOI : 10.5802/crmath.325

Classification : 14L10, 22E35, 11F85, 11J81

Affiliations des auteurs :

Duc Hiep Pham ¹

¹ University of Education, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Duc Hiep Pham},
     title = {$p$-adic non-commutative analytic subgroup theorem},
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     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.325},
     language = {en},
}

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Duc Hiep Pham. $p$-adic non-commutative analytic subgroup theorem. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 933-936. doi : 10.5802/crmath.325. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.325/

Bibliographie
Cité par

[1] Alan Baker; Gisbert Wüstholz Logarithmic Forms and Diophantine Geometry, New Mathematical Monographs, 9, Cambridge University Press, 2007 | Zbl

[2] Nicolas Bourbaki Elements of Mathematics. Lie groups and Lie algebras. Part I: Chapters 1-3. English translantion, Actualités Scientifiques et Industrielles, Addison-Wesley Publishing Group, 1975

[3] Clemens Fuchs; Duc Hiep Pham The $p$ -adic analytic subgroup theorem revisited, $p$ -Adic Numbers Ultrametric Anal. Appl., Volume 7 (2015) no. 2, pp. 143-156

[4] James S. Milne Algebraic Groups. The theory of group schemes of finite type over a field, Cambridge Studies in Advanced Mathematics, 170, Cambridge University Press, 2017

[5] Peter Schneider $p$ -adic Lie groups, Grundlehren der Mathematischen Wissenschaften, Springer, 2011

[6] Paula Tretkoff Periods and Special Functions in Transcendence, Advanced Textbooks in Mathematics, World Scientific, 2017

[7] Gisbert Wüstholz Some remarks on a conjecture of Waldschmidt, Approximations diophantiennes et nombres transcendants (Progress in Mathematics), Volume 31, Birkhäuser, 1983, pp. 329-336

[8] Gisbert Wüstholz Multiplicity estimates on group varieties, Ann. Math., Volume 129 (1989), pp. 471-500

[9] Gisbert Wüstholz Algebraische Punkte auf Analytischen Untergruppen algebraischer Gruppen, Ann. Math., Volume 129 (1989), pp. 501-517

[10] Gisbert Wüstholz Elliptic and abelian period spaces, Acta Arith., Volume 198 (2021), pp. 329-357

[11] Andrei Yafaev Non-commutative analytic subgroup theorem, J. Number Theory, Volume 230 (2022), pp. 233-237

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