Stable reduction of three point covers

 Access to full text

 Full (PDF)

 Access to full text

1. A. Abbes, Réduction semi–stable des courbes d’après Artin, Deligne, Grothendieck, Mumford, Saito, Winters,.... Courbes semi-stables et groupe fondamental en géometrie algébrique (J.-B. Bost, F. Loeser, and M. Raynaud, eds.), Prog. in Math., vol. 187, Birkhäuser, 2000, 59–108. Zbl0978.14031MR1768094
2. S. Beckmann, Ramified primes in the field of moduli of branched coverings of curves. J. of Algebra 125 (1989), 236–255. Zbl0698.14024MR1012673
3. G.V. Belyi, On Galois extensions of a maximal cyclotomic field. Math. USSR Izw. 14 (1980), no. 2, 247–256. Zbl0429.12004MR534593
4. I.I. Bouw, S. Wewers, Stable reduction of modular curves. Modular curves and abelian varieties (J. Cremona et.al., ed.), Progress in Math., no. 224, Birkhäuser, 1–22. Zbl1147.11316MR2058639
5. R.F. Coleman, On the components of $X_0\left(p^n\right)$. J. Number Theory 110 (2005), no. 1, 3–21. Zbl1108.14022MR2114670
6. P. Dèbes, J.-C. Douai, Algebraic covers: Field of moduli versus field of definition. Ann. Sci. École Norm. Sup. 30 (1997), 303–338. Zbl0906.12001MR1443489
7. P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus. Publ. Math. IHES 36 (1969), 75–109. Zbl0181.48803MR262240
8. P. Deligne, M. Rapoport, Les schémas de modules de courbes elliptiques. Modular functions of one variable II, LNM, no. 349, Springer-Verlag, 1972, 143–316. Zbl0281.14010MR337993
9. B. Edixhoven, Minimal resolution and stable reduction of $X_0\left(N\right)$. Ann. Inst. Fourier 40 (1990), no. 1, 31–67. Zbl0679.14009MR1056773
10. A. Grothendieck, Revêtement étales et groupe fondamental (SGA I). LNM, no. 224, Springer–Verlag, 1971. MR354651
11. Y. Henrio, Arbres de Hurwitz et automorphismes d’ordre $p$ des disques et des couronnes $p$-adic formels. To appear in: Compositio Math., available at arXiv:math.AG/0011098, 2000. 
12. —, Disque et couronnes ultramétriques. Courbes semi-stables et groupe fondamental en géometrie algébrique (J.-B. Bost, F. Loeser, and M. Raynaud, eds.), Prog. in Math., vol. 187, Birkhäuser, 2000, 7–18. MR1768107
13. B. Köck, Belyi’s theorem revisited. arXiv:math.AG/0108222. 
14. C. Lehr, M. Matignon, Wild monodromy and automorphisms of curves. Proceedings of the 2003 Workshop on Cryptography and Related Mathematics, Chuo University, 2003, available at http://www.math.u-bordeaux.fr/~matignon. Zbl1116.14020
15. Q. Liu, Reduction and lifting of finite covers of curves. Proceedings of the 2003 Workshop on Cryptography and Related Mathematics, Chuo University, 2003, available at http://www.math.u-bordeaux.fr/liu, 161–180. 
16. G. Malle, B. H. Matzat, Inverse Galois theory. Monographs in Mathematics, Springer, 1999. Zbl0940.12001MR1711577
17. F. Orgogozo, I. Vidal, Le théorèm de spécialisation du groupe fondamental. Courbes semi-stables et groupe fondamental en géometrie algébrique (J.-B. Bost, F. Loeser, and M. Raynaud, eds.), Prog. in Math., vol. 187, Birkhäuser, 2000, 169–184. Zbl0978.14033MR1768100
18. M. Raynaud, $p$-groupes et réduction semi-stable des courbes. Grothendieck Festschrift III (P. Cartier, ed.), Progress in Math., no. 88, Birkhäuser, 1990, 179–197. Zbl0722.14013MR1106915
19. —, Revêtement de la droite affine en caractéristique $p\>0$ et conjecture d’Abhyankar. Invent. Math. 116 (1994), 425–462. Zbl0798.14013MR1253200
20. —, Spécialisation des revêtements en caractéristique $p\>0$. Ann. Sci. École Norm. Sup. 32 (1999), no. 1, 87–126. MR1670532
21. L. Schneps (ed.), The grothendieck theory of dessins d’enfants. London Math. Soc. Lecture Note Series, no. 200, Cambridge Univ. Press, 1994. Zbl0798.00001MR1305393
22. H. Völklein, Groups as Galois groups. Cambridge Studies in Adv. Math., no. 53, Cambridge Univ. Press, 1996. Zbl0868.12003MR1405612
23. S. Wewers, Formal deformations of curves with group scheme action. arXiv:math.AG/0212145, to appear in: Ann. Inst. Fourier. Zbl1079.14006MR2157165
24. —, Deformation of tame admissible covers of curves. Aspects of Galois theory (H. Völklein, ed.), London Math. Society Lecture Notes Series, no. 256, Cambridge Univ. Press, 1999, 239–282. Zbl0995.14008MR1708609
25. —, Reduction and lifting of special metacyclic covers. Ann. Sci. École Norm. Sup. 36 (2003), 113–138. Zbl1042.14005MR1987978
26. —, Three point covers with bad reduction. J. Amer. Math. Soc. 16 (2003), no. 4, 991–1032. Zbl1062.14038MR1992833