Théorie des nombres
p-adic non-commutative analytic subgroup theorem
Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 933-936.

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].

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DOI : 10.5802/crmath.325
Classification : 14L10, 22E35, 11F85, 11J81
Pham, Duc Hiep 1

1 University of Education, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam
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Pham, Duc Hiep. $p$-adic non-commutative analytic subgroup theorem. Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 933-936. doi : 10.5802/crmath.325. http://www.numdam.org/articles/10.5802/crmath.325/

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

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

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

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

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

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

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

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

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

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

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