In the week of August, 16th-20th of 2004, we organized a workshop about “Automorphisms of Curves” at the Lorentz Center in Leiden. The programme included two “problem sessions”. Some of the problems presented at the workshop were written down; this is our edition of these refereed and revised papers. Edited by Gunther Cornelissen and Frans Oort with contributions of I. Bouw; T. Chinburg; G. Cornelissen; C. Gasbarri; D. Glass; C. Lehr; M. Matignon; F. Oort; R. Pries; S. Wewers.
@article{RSMUP_2005__113__129_0, author = {Cornelissen, Gunther and Oort, Frans}, title = {Problems from the workshop on Automorphisms of Curves (Leiden, August, 2004)}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, volume = {113}, year = {2005}, pages = {129-177}, mrnumber = {2168985}, zbl = {1167.14312}, language = {en}, url = {http://dml.mathdoc.fr/item/RSMUP_2005__113__129_0} }
Cornelissen, Gunther; Oort, Frans. Problems from the workshop on Automorphisms of Curves (Leiden, August, 2004). Rendiconti del Seminario Matematico della Università di Padova, Tome 113 (2005) pp. 129-177. http://gdmltest.u-ga.fr/item/RSMUP_2005__113__129_0/
[1] Geometry of Algebraic Curves, Number 267 in Grundlehren. Springer, 1985. | MR 770932 | Zbl 0559.14017
- - - ,[2] Alternating groups as monodromy groups in positive characteristic, Math. AG/0402436, to appear in Pacific J. Math. | MR 2200250 | Zbl 1111.14021
- ,[3] Realizing alternating groups as monodromy groups of genus one covers, Proc. Amer. Math. Soc., 129 (2000), pp. 111-119. | MR 1784019 | Zbl 0978.30026
- - ,[4] The inverse Galois problem and rational points on moduli spaces, Math. Ann., 290 (1991), pp. 771-800. | MR 1119950 | Zbl 0763.12004
- ,[5] Hurwitz schemes and the irreducibility of the moduli of algebraic curves, Ann. of Math. 90 (1969), pp. 542-575. | MR 260752 | Zbl 0194.21901
,[6] Moduli of curves, Number 187 in GTM. Springer, 1998. | MR 1631825 | Zbl 0913.14005
- ,[7] The monodromy group of a function on a general curve, Math. AG/0304130, to appear in Israel J. Math, 2003. | MR 2063042 | Zbl 1075.14027
- ,[8] Finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental group, Preprint. | MR 2073193 | Zbl 1100.14021
,[9] DemusÏkin groups with group actions and applications to deformations of Galois representations, Compositio Math., 121 (2000), pp. 109-154. | MR 1757878 | Zbl 0952.11009
,[10] Explicit construction of universal deformation rings, in Modular forms and Fermat's Last Theorem, G. Cornell, J. H. Silverman - G. Stevens (eds.), Springer, New York, Berlin, Heidelberg (1977), pp. 313- 326. | MR 1638482 | Zbl 0907.13010
- ,[11] Obstructions locales au relèvement de revêtements galoisiens de courbes lisses, C. R. Acad. Sci. Paris Sér. I Math. 326, no. 1 (1998), pp. 55-58. | MR 1649485 | Zbl 0952.14018
,[12] Déformations formelles des revêtements sauvagement ramifiés de courbes algébriques, Invent. Math., 141 (2000), pp. 195-238. | MR 1767273 | Zbl 0993.14014
- ,[13] The local lifting problem for dihedral groups, Math. AG/0409395.
- ,[14] Equivariant deformation of Mumford curves and of ordinary curves in positive characteristic, Duke Math. J., 116 (2003), pp. 431-470. | MR 1958094 | Zbl 1092.14032
- ,[15] Relèvements des revêtements de courbes faiblement ramifiés, Math. AG/0412189. | Zbl 1108.14024
- ,[16] p-groupes abéliens de type (p; Á Á Á ; p) et disques ouverts p-adiques, Manuscripta Math., 99, no. 1 (1999), pp. 93-109. | MR 1697205 | Zbl 0953.12004
,[17] p-ranks and automorphism groups of algebraic curves, Trans. Amer. Math. Soc., 303 (1987), pp. 595-607. | MR 902787 | Zbl 0644.14010
,[18] On the deformation of Artin-Schreier to Kummer, Ann. Sci. École Norm. Sup. (4) 22, no. 3 (1989), pp. 345-375. | Numdam | MR 1011987 | Zbl 0714.14024
- - ,[19] Relèvement des actions de (Z=2)2 , preprint (2004).
,[20] Flat vector bundles and the fundamental group in non-zero characteristics. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (1975). | Numdam | MR 382271 | Zbl 0322.14009
,[21] Vektorbndel auf Kurven und Darstellungen der algebraischen Fundamentalgruppe, Math. Z., 156, no. 1 (1977), pp. 73-83. | MR 472827 | Zbl 0349.14018
- ,[22] On the representations of the fundamental group, Compositio Math., 33, no. 1 (1976), pp. 29-41. | Numdam | MR 417179 | Zbl 0337.14016
,[23] Subvarieties of Moduli Space. Inventiones Mathematicae, 29 (1974), pp. 95-119. | MR 424813 | Zbl 0259.14011
,[24] Complete subvarieties of moduli spaces and the Prym map, to appear in J. Reine Angew. Math. | MR 2084584 | Zbl 1075.14023
- ,[25] Hyperelliptic curves with prescribed p-torsion, accepted by Manuscripta. | Zbl 1093.14039
- ,[26] Lectures on Hilbert modular varieties and modular forms, volume 14 of CRM Monograph Series, American Mathematical Society, Providence, RI, 2002. With the assistance of Marc-Hubert Nicole. | MR 1863355 | Zbl 0986.11037
,[27] Class number of a definite quaternion with prime discriminant, Proc. Nat. Acad. Sci. USA, 44 (1958), pp. 312-314. | MR 98728 | Zbl 0081.03601
,[28] Idempotent relations and factors of Jacobians, Math. Ann., 284 (2) (1989) pp. 307-327. | MR 1000113 | Zbl 0652.14011
- ,[29] Hyperelliptic supersingular curves. In Arithmetic algebraic geometry (Texel, 1989), volume 89 of Progr. Math., pages 247-284. Birkhäuser Boston, Boston, MA, 1991. | MR 1085262 | Zbl 0820.14018
,[30] On the Jacobian varieties of hyperelliptic curves over fields of characteristic p > 2, J. Algebra, 52 (2) (1978), pp. 378-410. | MR 491717 | Zbl 0404.14008
,[31] Order p automorphisms of the open disc of a p-adic field, J. Amer. Math. Soc., 12 (1999), pp. 269-303. | MR 1630112 | Zbl 0923.14007
- ,[32] Arbres de Hurwitz et automorphismes d'ordre p des disques et des couronnes p-adiques formels, Thèse Université Bordeaux I, 1999.
,[33] Endliche Gruppen I, Die Grundlehren der Mathematischen Wissenschaften, Band 134 Springer-Verlag, Berlin-New York 1967. | MR 224703 | Zbl 0217.07201
,[34] Reduction of p-cyclic Covers of the Projective Line, Manuscripta Math., 106 2 (2001) 151-175. | MR 1865562 | Zbl 1065.14508
,[35] Automorphism groups for p-cyclic covers of the affine line, to appear in Compositio Math. http://www.math.u-bordeaux1.fr/ ~matignon/preprints.html | MR 2157136 | Zbl 1083.14028
- ,[36] Curves with a big p-group action, in preparation.
- ,[37] Wild monodromy and automorphisms of curves, conference proceedings, Tokyo, (2002) (T. Sekiguchi, N. Suwa, editors), to appear. Available on http://www.math.u-bordeaux1.fr/~matignon/ | MR 2272976
, ,[38] Wild monodromy and automorphisms of curves, in preparation. | Zbl 1116.14020
- ,[39] Vers un algorithme pour la réduction stable des revêtements p-cycliques de la droite projective sur un corps p-adique, Mathematische Annalen, 325, (2003), pp. 323-354. | MR 1962052 | Zbl 1051.14031
,[40] p-ranks and automorphism groups of algebraic curves, Trans. Amer. Math. Soc., 303 (1987), pp. 595-607. | MR 902787 | Zbl 0644.14010
,[41] p-groupes et réduction semi-stable des courbes, The Grothendieck Festschrift, Vol III, Progress in Mathematics, 88 (1990), Birkhäuser, pp. 179-197. | MR 1106915 | Zbl 0722.14013
,[42] Spécialisation des revêtements en caractéristique p > 0, Ann. Scient. Ec. Norm. Sup., 32 (4) (1999), pp. 87-126. | Numdam | MR 1670532 | Zbl 0999.14004
,[43] Group theory II, Grundlehren der Mathematischen Wissenschaften 248, Springer-Verlag, New York, 1986. | MR 815926 | Zbl 0586.20001
,[44] Obstructions locales au relêvement de revêtements galoisiens de courbes lisses, C. R. Acad. Sci. Paris Sér. I Math., 326, no. 1 (1998), pp. 55-58. | MR 1649485 | Zbl 0952.14018
,[45] The local lifting problem for dihedral groups, preprint Math. AG/0409395. | MR 2254623 | Zbl 1108.14025
, - ,[46] Liftings of Galois covers of smooth curves, Compositio Math., 113 (1998), pp. 239-274. | MR 1645000 | Zbl 0923.14006
- ,[47] Order p automorphisms of the open disc of a p-adic field, J. Amer. Math. Soc., 12 (1999), pp. 269-303. | MR 1630112 | Zbl 0923.14007
- ,[48] Arbres de Hurwitz et automorphismes d'ordre p des disques et des couronnes p-adiques formels, Thèse Université Bordeaux I, 1999.
,[49] Reduction and lifting of finite covers of curves, Proceedings of the 2003 Workshop on Cryptography and Related Mathematics, Chuo University (2003), pp. 161-180, available at http://www.math.u-bordeaux1.fr/~liu/preprints.html
,[50] p-groupes abeliens de type (p; . . . ; p) et disques ouverts p-adiques, Manuscripta Math., 99 (1999), pp. 93-109. | MR 1697205 | Zbl 0953.12004
,[51] Autour d'une conjecture de F. Oort sur le relèvement de revêtements galoisiens de courbes, French version for the Limoges seminar (2003) of my MSRI lecture in the workshop on Constructive Galois Theory (1999), available at http://www.math.u-bordeaux1.fr/~matignon/preprints.html
,[52] Lifting (Z=2Z)2 -actions, (2003) available at http://www.math.u-bordeaux1.fr/~matignon/preprints.html
,[53] Fp-espaces vectoriels de formes différentielles logarithmiques en caractéristique > 0 et automorphismes du disque ouvert p-adique, J. Number Theory, 97 no. 1 (2002), pp. 58-94. | MR 1939137 | Zbl 1076.14504
,[54] Relèvement en caractéristique zéro d'actions de groupes abéliens de type (p; :::; p), Thèse Université Bordeaux I, 2002.
,[55] Relèvement des actions de (Z=2Z)2 , Projet de note aux CRAS (2004).
,[56] A note on extensions of algebraic and formal groups. IV. Kummer-Artin-Schreier-Witt theory of degree p2 , Tohoku Math. J. (2) 53, no. 2 (2001), pp. 203-240. | MR 1829979 | Zbl 1073.14546
- ,[57] A note on extensions of algebraic and formal groups. V, Japan. J. Math. (N.S.) 29 no. 2 (2003), pp. 221-284. | MR 2035540 | Zbl 1075.14045
- ,[58] On the unified Kummer-Artin-Schreier-Witt theory, Prépublication Université de Bordeaux (1999).
- ,[59] Moduli of supersingular abelian varieties, Lecture Notes Math. 1680, Springer - Verlag, 116 (1998), pp. ??? | MR 1611305 | Zbl 0920.14021
- ,[60] Complete subvarieties of moduli spaces and the Prym map, In arXiv: math.AG/0305334 [to appear in J. Reine Angew. Math.] | MR 2084584 | Zbl 1075.14023
- ,[61] On the existence of supersingular curves of given genus, J. Reine Angew. Math., 458 (1995), pp. 53-61. | MR 1310953 | Zbl 0819.11022
- ,[62] Hyperelliptic curves with prescribed p-torsion, [To appear in Masnuscr. Math.] | MR 2154252 | Zbl 1093.14039
- ,[63] Questions on p-torsion of hyperelliptic curves, [This volume]
- ,[64] Slope filtrations of F-crystals, Journ. Géom. Alg. Rennes 1978. Vol. I, Astérisque 63, Soc. Math. France 1979; pp. 113-163. | MR 563463 | Zbl 0426.14007
,[65] The theory of commutative formal groups over fields of finite characteristic, Usp. Math., 18 (1963), pp. 3-90; Russ. Math. Surveys, 18 (1963), pp. 1-80. | MR 157972 | Zbl 0128.15603
,[66] Jacobian varieties, Chapter 7 in: Arithmetic geometry (Ed. G. Cornell - J. H. Silverman. Springer - Verlag, 1986; pp. 167-212. | MR 861976 | Zbl 0604.14018
,[67] Moduli of abelian varieties, Ann. Math., 112 (1980), pp. 413-439. | MR 595202 | Zbl 0483.14010
- ,[68] Hyperelliptic supersingular curves, In: Arithmetic Algebraic Geometry (Texel 1989) (Ed. G. van der Geer, F. Oort, J. Steenbrink). Progress Math. 89, Birkhäuser 1991; pp. 247-284. | MR 1085262 | Zbl 0820.14018
,[69] Newton polygons and formal groups: conjectures by Manin and Grothendieck, Ann. Math., 152 (2000), pp. 183-206. | MR 1792294 | Zbl 0991.14016
,[70] A stratification of a moduli space of polarized abelian varieties, In: Moduli of abelian varieties (Ed. C. Faber, G. van der Geer, F. Oort). Progress Math., 195, Birkhäuser Verlag 2001; pp. 345-416. | MR 1827027 | Zbl 1052.14047
,[71] Newton polygon strata in the moduli space of abelian varieties, In: Moduli of abelian varieties (Ed. C. Faber, G. van der Geer, F. Oort). Progress Math., 195, Birkhäuser Verlag 2001; pp. 417-440. | MR 1827028 | Zbl 1086.14037
,[72] Principally polarized abelian varieties of dimension two or three are Jacobian varieties, Journ. Fac. Sc. Univ. Tokyo, Sec. IA, 20 (1973), pp. 377-381. | MR 364265 | Zbl 0272.14008
- ,[73] Invariants of curves and Jacobians in positive characteristic, PhD-thesis Amsterdam 2004.
,[74] Hyperelliptic curves in characteristic 2, Int. Math. Res. Not. 17 (2002), pp. 905-917. | MR 1899907 | Zbl 1034.14013
- ,[75] Families of supersingular curves in characteristic 2, Math. Res. Lett., 9 (2002), pp. 639-650. | MR 1906067 | Zbl 1057.14037
- ,[76] Zum Beweis des Torellischen Satzes, Nachr. Akad. Göttingen, Math.-Phys. Kl. (1957), pp. 33-53. See êII [1957a]. | MR 89483 | Zbl 0079.37002
,[77] On the number of automorphisms of a closed Riemann surface, Transact. AMS 131 (1968), pp. 398-408. | MR 222281 | Zbl 0179.11401
,[78] Topics in the theory of Riemann surfaces, Lect. Notes Math. 1595, Springer - Verlag, 1994. | MR 1329541 | Zbl 0820.30002
,[79] On a theorem of Hurwitz, Proceed. Glasgow Math. Assoc., 5 (1961), pp. 90-96. | MR 146724 | Zbl 0134.16603
,[80] A bound for the number of automorphisms of a compact Riemann surface, Journ. London Math. Soc. 44 (1969), pp. 265-272. | MR 236378 | Zbl 0164.37904
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