Wild ramification of moduli spaces for curves or for abelian varieties
Compositio Mathematica (1985)
- Volume: 54, Issue: 3, page 331-372
- ISSN: 0010-437X
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topSekiguchi, Tsutomu. "Wild ramification of moduli spaces for curves or for abelian varieties." Compositio Mathematica 54.3 (1985): 331-372. <http://eudml.org/doc/89705>.
@article{Sekiguchi1985,
author = {Sekiguchi, Tsutomu},
journal = {Compositio Mathematica},
keywords = {positive characteristic; coarse moduli space; field of moduli for a principally polarized abelian variety; smooth curve},
language = {eng},
number = {3},
pages = {331-372},
publisher = {Martinus Nijhoff Publishers},
title = {Wild ramification of moduli spaces for curves or for abelian varieties},
url = {http://eudml.org/doc/89705},
volume = {54},
year = {1985},
}
TY - JOUR
AU - Sekiguchi, Tsutomu
TI - Wild ramification of moduli spaces for curves or for abelian varieties
JO - Compositio Mathematica
PY - 1985
PB - Martinus Nijhoff Publishers
VL - 54
IS - 3
SP - 331
EP - 372
LA - eng
KW - positive characteristic; coarse moduli space; field of moduli for a principally polarized abelian variety; smooth curve
UR - http://eudml.org/doc/89705
ER -
References
top- [1] W. Baily: On the theory of θ-functions, the moduli of abelian varieties, and the moduli of curves. Annals of Math.75 (1962) 342-381. Zbl0147.39702
- [2] C.W. Curtis and I. Reiner: Representation Theory of Finite Groups and Associative Algebras. New York: Interscience Publishers (1962). Zbl0131.25601MR144979
- [3] N. Bourbaki: Algèbre commutative. Eléments de Math.27, 28, 30, 31. Hermann: Paris (1961-1965).
- [4] P. Deligne and D. Mumford: The irreducibility of the space of curves of given genus. Publ. Math. IHES36 (1969) 75-110. Zbl0181.48803MR262240
- [5] A. Grothendieck: Fondéments de la géométrie algébrique. Séminaire Bourbaki 1957-1962.Secrétariat Math.paris (1962). Refered to as FGA. Zbl0239.14002MR146040
- [6] A. Grothendieck and J. Dieudonné: Eléments de géométrie algébrique. Publ. Math. IHES4, 8, 11, 17, 20, 24, 28, 32, 1960-1972. Refered to as EGA. Zbl0203.23301
- [7] A. Grothendieck et al.: Séminaire de géométrie algébrique 1. Lecture Notes in Math. Vol. 224. Berlin-Heidelberg-New York: Springer (1971). Refered to as SGA 1. Zbl0234.14002
- [8] H. Hasse: Theorie der relativ-zyklischen algebraischen Funktionen-Körper, insbesondere bei endlichen Konstanten-Körper. Journ. reine angew. Math. (Crelle) 172 (1935) 37-54. Zbl0010.00501JFM60.0097.01
- [9] S. Koizumi: The fields of moduli for polarized abelian varieties and for curves. Nagoya Math. J.48 (1972) 37-55. Zbl0246.14006MR352095
- [10] O.A. Laudal and K. Lønsted: Deformations of curves I, moduli for hyperelliptic curves. In: Algebraic Geometry. Proceedings Tromso, Norway 1977. Lecture Notes in Math. Vol. 687, pp. 150-167. Berlin- Heidelberg-New York: Springer (1978). Zbl0422.14014MR527233
- [11] K. Lønsted: The hyperelliptic locus with special reference to characteristic two. Math. Ann.222 (1976) 55-61. Zbl0314.14009MR407030
- [12] K. Lønsted and S.L. Kleiman: Basics on families of hyperelliptic curves. Comp. Math.38 (1979) 83-111. Zbl0406.14017MR523266
- [13] H. Matsumura: Commutative Algebra. New York: W.A. Benjamin (1970). Zbl0211.06501MR266911
- [14] T. Matsusaka: Polarized varieties, fields of moduli, and generalized Kummer varieties of polarized abelian varieties. Amer. J. Math.80 (1958) 45-82. Zbl0085.15304MR94360
- [15] T. Matsusaka: On a theorem of Torelli. Amer. J. Math.80 (1958) 784-800. Zbl0100.35602MR97398
- [16] W. Messing: The crystals associated to Barsotti-Tate groups; with applications to abelian schemes. Lecture Notes in Math. Vol. 264. Berlin-Heidelberg -New York: Springer (1972). Zbl0243.14013MR347836
- [17] D. Mumford: Geometric Invariant Theory. Ergebnisse. Berlin- Heidelberg-New York: Springer (1965). Zbl0147.39304MR214602
- [18] D. MumfordAbelian varieties. Tata Inst. Studies in Math. Oxford University Press (1970). Zbl0223.14022MR282985
- [19] M. Nagata: Local rings. Interscience Tracts in Pure & Applied Math. 13. New York: J. Wiley (1962). Zbl0123.03402MR155856
- [20] F. Oort: Finite group schemes, local moduli for abelian varieties and lifting problems. In: Algebraic Geometry, Oslo (1970) pp. 223-254. Wolters-Noordhoff (1972). Also: Comp. Math.23 (1972) 265-296. Zbl0223.14024MR301026
- [21] F. Oort: Singularities of coarse moduli schemes. Sém. Dubreil29 (1975/1976). Lecture Notes in Math. Vol. 586, pp. 61-76. Berlin -Heidelberg-New York: Springer (1977). Zbl0349.14003MR518011
- [22] F. Oort and J. Steenbrink: The local Torelli problem for algebraic curves. J. de Geometrie Algebrique Angers (1979) A. Beauville editor, Sijthoff & Noordhoff (1980) pp. 157-203. Zbl0444.14007MR605341
- [23] F. Oort and K. Ueno: Principally polarized abelian varieties of dimension two or three are jacobian varieties. J. Fac. Sci. Univ. Tokyo, Section IA, Math. 20 (1973) 377-381. Zbl0272.14008MR364265
- [24] B.R. Peskin: Quotient-singularities in characteristic p. Thesis, M.I.T. (1980).
- [25] H. Popp: The singularities of the moduli scheme of curves. J. Number Theory1 (1969) 90-107. Zbl0175.18503MR237492
- [26] T. Sekiguchi: On the fields of rationality for curves and for abelian varieties. Bull. Facult. Sci. & Eng. Chuo Univ.23 (1980) 35-41. Zbl0473.14013MR626110
- [27] T. Sekiguchi: The coincidence of fields of moduli for nonhyperelliptic curves and for their jacobian varieties. Nagoya Math. J.82 (1981) 57-82. Zbl0423.14017MR618808
- [28] T. Sekiguchi: On the fields of rationality for curves and for their jacobian varieties. Nagoya Math. J.88 (1982) 197-212. Zbl0473.14012MR683250
- [29] G. Shimura: On the field of rationality for an abelian variety. Nagoya Math. J.45 (1972) 167-178. Zbl0243.14012MR306215
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