The present article is based on the four hours mini-courses “Introduction to Mono-anabelian Geometry” which the author gave at the conference “Fundamental Groups in Arithmetic Geometry” (Paris, 2016). The purpose of the present article is to introduce mono-anabelian geometry by focusing on mono-anabelian geometry for mixed-characteristic local fields, which provides elementary but nontrivial examples of typical arguments in the study of mono-anabelian geometry.
Cet article est basé sur les 4 heures de mini-cours « Introduction to Mono-anabelian Geometry » que l’auteur a données lors de la conférence « Fundamental Groups in Arithmetic Geometry » (Paris, 2016). L’objectif est de présenter la géométrie mono-anabélienne en se concentrant sur les corps locaux de caractéristique mixte ce qui permet de fournir des exemples élémentaires mais non-triviaux du type d’arguments présents dans l’étude de géométrie mono-anabélienne.
Published online:
Keywords: mono-anabelian geometry, MLF, mono-anabelian reconstruction algorithm, MLF-pair, cyclotomic synchronization, Kummer poly-isomorphism, mono-anabelian transport
Yuichiro Hoshi 1
@article{PMB_2021____5_0, author = {Yuichiro Hoshi}, title = {Introduction to {Mono-anabelian} {Geometry}}, journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres}, pages = {5--44}, publisher = {Presses universitaires de Franche-Comt\'e}, year = {2021}, doi = {10.5802/pmb.42}, language = {en}, url = {https://pmb.centre-mersenne.org/articles/10.5802/pmb.42/} }
TY - JOUR AU - Yuichiro Hoshi TI - Introduction to Mono-anabelian Geometry JO - Publications mathématiques de Besançon. Algèbre et théorie des nombres PY - 2021 SP - 5 EP - 44 PB - Presses universitaires de Franche-Comté UR - https://pmb.centre-mersenne.org/articles/10.5802/pmb.42/ DO - 10.5802/pmb.42 LA - en ID - PMB_2021____5_0 ER -
%0 Journal Article %A Yuichiro Hoshi %T Introduction to Mono-anabelian Geometry %J Publications mathématiques de Besançon. Algèbre et théorie des nombres %D 2021 %P 5-44 %I Presses universitaires de Franche-Comté %U https://pmb.centre-mersenne.org/articles/10.5802/pmb.42/ %R 10.5802/pmb.42 %G en %F PMB_2021____5_0
Yuichiro Hoshi. Introduction to Mono-anabelian Geometry. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2021), pp. 5-44. doi : 10.5802/pmb.42. https://pmb.centre-mersenne.org/articles/10.5802/pmb.42/
[1] A note on the geometricity of open homomorphisms between the absolute Galois groups of -adic local fields, Kodai Math. J., Volume 36 (2013) no. 2, pp. 284-298 | MR | Zbl
[2] Mono-anabelian reconstruction of number fields, RIMS Kôkyûroku Bessatsu, Volume B76 (2019), pp. 1-77 | Zbl
[3] On the characterization of local fields by their absolute Galois groups, J. Number Theory, Volume 11 (1979) no. 1, pp. 1-13 | DOI | MR | Zbl
[4] A version of the Grothendieck conjecture for -adic local fields, Int. J. Math., Volume 8 (1997) no. 4, pp. 499-506 | DOI | MR | Zbl
[5] Topics in absolute anabelian geometry I: generalities, J. Math. Sci., Tokyo, Volume 19 (2012) no. 2, pp. 139-242 | MR | Zbl
[6] Topics in absolute anabelian geometry III: global reconstruction algorithms, J. Math. Sci., Tokyo, Volume 22 (2015) no. 4, pp. 939-1156 | MR | Zbl
[7] The mathematics of mutually alien copies: from Gaussian integrals to inter-universal Teichmüller theory, RIMS Kôkyûroku Bessatsu, Volume B84 (2021), pp. 23-192 | Zbl
[8] Algebraic number theory, Grundlehren der Mathematischen Wissenschaften, 322, Springer, 1992 | Zbl
[9] Cohomology of number fields, Grundlehren der Mathematischen Wissenschaften, 323, Springer, 2008 | DOI | Zbl
[10] Finite index subgroups in profinite groups, C. R. Math. Acad. Sci. Paris, Volume 337 (2003) no. 5, pp. 303-308 | DOI | MR | Zbl
[11] Local class field theory, Algebraic Number Theory, Academic Press Inc., 1965, pp. 128-161
[12] -divisible groups, Proc. Conf. Local Fields (Driebergen, 1966), Springer, 1967, pp. 158-183 | DOI | Zbl
[13] A counterexample for the local analogy of a theorem by Iwasawa and Uchida, Proc. Japan Acad., Volume 52 (1976) no. 6, pp. 276-278 | MR | Zbl
Cited by Sources: