Comptes Rendus
Number theory
On sections of arithmetic fundamental groups of open p-adic annuli
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 291-296.

We show the non-existence of sections of arithmetic fundamental groups of open p-adic annuli of small radii. This implies the non-existence of sections of arithmetic fundamental groups of formal boundaries of formal germs of p-adic curves.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.303
Mohamed Saïdi 1

1 College of Engineering, Mathematics, and Physical Sciences, University of Exeter, Harrison Building, North Park Road, EXETER EX4 4QF, United Kingdom
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{CRMATH_2022__360_G3_291_0,
     author = {Mohamed Sa{\"\i}di},
     title = {On sections of arithmetic fundamental groups of open $p$-adic annuli},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {291--296},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.303},
     language = {en},
}
TY  - JOUR
AU  - Mohamed Saïdi
TI  - On sections of arithmetic fundamental groups of open $p$-adic annuli
JO  - Comptes Rendus. Mathématique
PY  - 2022
SP  - 291
EP  - 296
VL  - 360
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.303
LA  - en
ID  - CRMATH_2022__360_G3_291_0
ER  - 
%0 Journal Article
%A Mohamed Saïdi
%T On sections of arithmetic fundamental groups of open $p$-adic annuli
%J Comptes Rendus. Mathématique
%D 2022
%P 291-296
%V 360
%I Académie des sciences, Paris
%R 10.5802/crmath.303
%G en
%F CRMATH_2022__360_G3_291_0
Mohamed Saïdi. On sections of arithmetic fundamental groups of open $p$-adic annuli. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 291-296. doi : 10.5802/crmath.303. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.303/

[1] Yves Aubry; Annamaria Iezzi On the Maximum Number of Rational Points on Singular Curves over Finite Fields, Mosc. Math. J., Volume 15 (2015) no. 4, pp. 615-627 | DOI | MR | Zbl

[2] Nicolas Bourbaki Eléments de mathématique. Algèbre commutative. Chapitre 9: Anneaux locaux noethériens complets, Masson, 1983

[3] Revêtements étales et groupe fondamental (Alexander Grothendieck, ed.), Lecture Notes in Mathematics, 224, Springer, 1971 | DOI

[4] Jochen Koenigsmann On the ‘Section Conjecture’ in anabelian geometry, J. Reine Angew. Math., Volume 588 (2005), pp. 221-235 | DOI | MR | Zbl

[5] Qing Liu Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics, 6, Oxford University Press, 2002 | Zbl

[6] Jürgen Neukirch; Alexander Schmidt; Kay Wingberg Cohomology of number fields (Grundlehren der Mathematischen Wissenschaften), Volume 323, 2000 | MR | Zbl

[7] Maxwell Rosenlicht Equivalence relations on algebraic curves, Ann. Math., Volume 56 (1952) no. 1, pp. 169-191 | DOI | MR | Zbl

[8] Mohamed Saïdi On the existence of non-geometric sections of arithmetic fundamental groups, Math. Z., Volume 277 (2014) no. 1-2, pp. 361-372 | DOI | MR | Zbl

[9] Mattia Talpo; Angelo Vistoli Deformation theory from the point of view of fibered categories, Handbook of moduli. Volume III (Advanced Lectures in Mathematics (ALM)), Volume 26, International Press, 2013, pp. 281-397 | MR | Zbl

Cited by Sources:

Comments - Policy