Abstract
In this article, we consider certain systems of derivation algebras related to Galois representations attached to fundamental groups of algebraic curves of positive genera and establish some stability property. This is a generalization of Ihara’s result in the case of genus zero.
Similar content being viewed by others
References
M. Asada and M. Kaneko,On the automorphism groups of some pro-l fundamental groups, Advanced Studies in Pure Mathematics12 (1987), 137–159.
V. G. Drinfel’d,On quasitriangular quasi-Hopf algebras and a group closely related with Gal(\(\bar Q/Q\)). Algebra i Analiz2 (1990), 149–181; English translation: Leningrad Mathematical Journal2 (1991), 829–860.
Y. Ihara,Profinite braid groups, Galois representations and complex multiplications, Annals of Mathematics123 (1986), 43–106.
Y. Ihara,Automorphisms of pure sphere braid groups and Galois representations, inThe Grothendieck Festschrift II, Progress in Mathematics87, 1991, pp. 353–373.
Y. Ihara,On the stable derivation algebra associated with some braid groups, Israel Journal of Mathematics80 (1992), 135–153.
Y. Ihara,Some arithmetic aspects of Galois actions on the pro-p fundamental group of P 1 − {0, 1, ∞}, inArithmetic Fundamental Groups and Noncommutative Algebra, Proceedings of Symposia in Pure Mathematics70 (2002), 247–273.
Y. Ihara and M. Kaneko,Pro-l pure braid groups of Riemann surfaces and Galois representations, Osaka Journal of Mathematics29 (1992), 1–19.
Y. Ihara and H. Nakamura,On deformation of maximally degenerate stable marked curves and Oda’s problem, Journal für die reine und angewandte Mathematik487 (1997), 125–151.
M. Kaneko,Certain automorphism groups of pro-l fundamental groups of punctured Riemann surfaces, Journal of the Faculty of Science of the University of Tokyo36 (1989), 363–372.
M. Matsumoto,On Galois representations on profinite braid groups of curves, Journal für die reine und angewandte Mathematik474 (1996), 169–219.
H. Nakamura,On exterior Galois representations associated with open elliptic curves, Journal of Mathematical Sciences of the University of Tokyo2 (1995), 197–231.
H. Nakamura,Coupling of universal monodromy representations of Galois-Teichmüller modular groups, Mathematische Annalen304 (1996), 99–119.
H. Nakamura and N. Takao,Galois regidity of pro-l pure braid groups of algebraic curves, Transactions of the American Mathematical Society350 (1998), 1079–1102.
H. Nakamura, N. Takao and R. Ueno,Some stability properties of Teichmüller modular function fields with pro-l weight structures, Mathematische Annalen302 (1995), 197–213.
H. Nakamura and H. Tsunogai,Some finiteness theorems on Galois centralizers in pro-l mapping class group, Journal für die reine und angewandte Mathematik441 (1993), 115–144.
T. Oda,The universal monodromy representations on the pro-nilpotent fundamental groups of algebraic curves, Mathematische Arbeitstagung (Neue Serie), Max-Planck-Institute preprint MPI/93-57, 9–15 June 1993.
J. P. Serre,Propriétés galoisiennes des points d’ordre fini des courbes elliptiques, Inventiones Mathematicae15 (1972), 259–331.
H. Tsunogai,On some derivations of Lie algebras related to Galois representations, Publications of the Research Institute for Mathematical Sciences, Kyoto University31 (1995), 113–134.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was partly supported by National Science Foundation Grant 09740041 and 12740026.
Rights and permissions
About this article
Cite this article
Tsunogai, H. The stable derivation algebras for higher genera. Isr. J. Math. 136, 221–250 (2003). https://doi.org/10.1007/BF02807199
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02807199