A refined version of Grothendieck’s anabelian conjecture for hyperbolic curves over finite fields
Authors:
Mohamed Saïdi and Akio Tamagawa
Journal:
J. Algebraic Geom. 27 (2018), 383-448
DOI:
https://doi.org/10.1090/jag/708
Published electronically:
March 29, 2018
MathSciNet review:
3803604
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Abstract |
References |
Additional Information
Abstract: In this paper we prove a refined version of a theorem by Tamagawa and Mochizuki on isomorphisms between (tame) arithmetic fundamental groups of hyperbolic curves over finite fields, where one “ignores” the information provided by a “small” set of primes.
References
- E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463
- Encyclopedic dictionary of mathematics. Vol. I–IV, 2nd ed., MIT Press, Cambridge, MA, 1987. Translated from the Japanese; Edited by Kiyosi Itô. MR 901762
- Alexander Grothendieck, Brief an G. Faltings, Geometric Galois actions, 1, London Math. Soc. Lecture Note Ser., vol. 242, Cambridge Univ. Press, Cambridge, 1997, pp. 49–58 (German). With an English translation on pp. 285–293. MR 1483108
- Shinichi Mochizuki, Absolute anabelian cuspidalizations of proper hyperbolic curves, J. Math. Kyoto Univ. 47 (2007), no. 3, 451–539. MR 2402513, DOI https://doi.org/10.1215/kjm/1250281022
- Shinichi Mochizuki, Topics in absolute anabelian geometry I: generalities, J. Math. Sci. Univ. Tokyo 19 (2012), no. 2, 139–242. MR 2987306
- Mohamed Saïdi and Akio Tamagawa, A prime-to-$p$ version of Grothendieck’s anabelian conjecture for hyperbolic curves over finite fields of characteristic $p>0$, Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, 135–186. MR 2512780, DOI https://doi.org/10.2977/prims/1234361157
- Mohamed Saïdi and Akio Tamagawa, On the anabelian geometry of hyperbolic curves over finite fields, Algebraic number theory and related topics 2007, RIMS Kôkyûroku Bessatsu, B12, Res. Inst. Math. Sci. (RIMS), Kyoto, 2009, pp. 67–89. MR 2605774
- Mohamed Saïdi and Akio Tamagawa, A refined version of Grothendieck’s birational anabelian conjecture for curves over finite fields, Adv. Math. 310 (2017), 610–662. MR 3620695, DOI https://doi.org/10.1016/j.aim.2017.02.010
- Akio Tamagawa, The Grothendieck conjecture for affine curves, Compositio Math. 109 (1997), no. 2, 135–194. MR 1478817, DOI https://doi.org/10.1023/A%3A1000114400142
References
- E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463
- Encyclopedic dictionary of mathematics. Vol. I–IV, translated from the Japanese, 2nd ed., edited by Kiyosi Itô, MIT Press, Cambridge, MA, 1987. MR 901762
- Alexander Grothendieck, Brief an G. Faltings, Geometric Galois actions, 1, with an English translation on pp. 285–293, London Math. Soc. Lecture Note Ser., vol. 242, Cambridge Univ. Press, Cambridge, 1997, pp. 49–58 (German). MR 1483108
- Shinichi Mochizuki, Absolute anabelian cuspidalizations of proper hyperbolic curves, J. Math. Kyoto Univ. 47 (2007), no. 3, 451–539. MR 2402513, DOI https://doi.org/10.1215/kjm/1250281022
- Shinichi Mochizuki, Topics in absolute anabelian geometry I: generalities, J. Math. Sci. Univ. Tokyo 19 (2012), no. 2, 139–242. MR 2987306
- Mohamed Saïdi and Akio Tamagawa, A prime-to-$p$ version of Grothendieck’s anabelian conjecture for hyperbolic curves over finite fields of characteristic $p>0$, Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, 135–186. MR 2512780, DOI https://doi.org/10.2977/prims/1234361157
- Mohamed Saïdi and Akio Tamagawa, On the anabelian geometry of hyperbolic curves over finite fields, Algebraic number theory and related topics 2007, RIMS Kôkyûroku Bessatsu, B12, Res. Inst. Math. Sci. (RIMS), Kyoto, 2009, pp. 67–89. MR 2605774
- Mohamed Saïdi and Akio Tamagawa, A refined version of Grothendieck’s birational anabelian conjecture for curves over finite fields, Adv. Math. 310 (2017), 610–662. MR 3620695, DOI https://doi.org/10.1016/j.aim.2017.02.010
- Akio Tamagawa, The Grothendieck conjecture for affine curves, Compositio Math. 109 (1997), no. 2, 135–194. MR 1478817, DOI https://doi.org/10.1023/A%3A1000114400142
Additional Information
Mohamed Saïdi
Affiliation:
College of Engineering, Mathematics, and Physical Sciences, University of Exeter, Harrison Building, North Park Road, Exeter EX4 4QF, United Kingdom
Email:
M.Saidi@exeter.ac.uk
Akio Tamagawa
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
MR Author ID:
362316
Email:
tamagawa@kurims.kyoto-u.ac.jp
Received by editor(s):
November 19, 2014
Received by editor(s) in revised form:
December 13, 2014
Published electronically:
March 29, 2018
Article copyright:
© Copyright 2018
University Press, Inc.
