Geodesic
On definition fields of an algebraic curve
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 219-230
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

It is considered such geometric invariants of an algebraic curve as the minimal number of crucial values of the rational functions and the minimal transcendence degree of the definition fields. The question is if the difference of these two invariants is always equal to 3 for any curve with the genus $g>0$. For curves defined over an algebraic number field the positive answer is given by Belyi's theorem. In the paper the positive answer is given for some other cases. 
@article{ZNSL_2014_430_a13,
     author = {A. L. Smirnov},
     title = {On definition fields of an algebraic curve},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {219--230},
     year = {2014},
     volume = {430},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a13/}
}
TY  - JOUR
AU  - A. L. Smirnov
TI  - On definition fields of an algebraic curve
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 219
EP  - 230
VL  - 430
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a13/
LA  - ru
ID  - ZNSL_2014_430_a13
ER  - 
%0 Journal Article
%A A. L. Smirnov
%T On definition fields of an algebraic curve
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 219-230
%V 430
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a13/
%G ru
%F ZNSL_2014_430_a13
A. L. Smirnov. On definition fields of an algebraic curve. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 219-230. http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a13/

[1] G. V. Belyi, “O`rasshireniyakh Galua maksimalnogo krugovogo polya”, Izv. AN SSSR, Ser. matem., 43:2 (1979), 267–276 | MR | Zbl

[2] G. V. Belyi, “Novoe dokazatelstvo teoremy o trekh tochkakh”, Matem. sbornik, 193:3 (2002), 21–24 | DOI | MR | Zbl

[3] F. Bogomolov, D. Husemoller, Geometric properties of curves defined over number fields, v. 1, MPI, Bonn, 2000

[4] F. Griffits, Dzh. Kharris, Printsipy algebraicheskoi geometrii, Mir, M., 1982 | MR

[5] R. Khartskhorn, Algebraicheskaya geometriya, Mir, M., 1981 | MR

[6] N. Katz, “Travaux de Laumon”, Sém. Bourbaki, (1987–1988), No. 691, Astérisque, 161–162, 1988, 105–132 | MR | Zbl

[7] A. L. Smirnov, O polyakh opredeleniya algebraicheskoi krivoi, Preprint 2/2013, POMI RAN