An analytic construction of degenerating curves over complete local rings

David Mumford

Compositio Mathematica (1972)

  • Volume: 24, Issue: 2, page 129-174
  • ISSN: 0010-437X

How to cite


Mumford, David. "An analytic construction of degenerating curves over complete local rings." Compositio Mathematica 24.2 (1972): 129-174. <>.

author = {Mumford, David},
journal = {Compositio Mathematica},
language = {eng},
number = {2},
pages = {129-174},
publisher = {Wolters-Noordhoff Publishing},
title = {An analytic construction of degenerating curves over complete local rings},
url = {},
volume = {24},
year = {1972},

AU - Mumford, David
TI - An analytic construction of degenerating curves over complete local rings
JO - Compositio Mathematica
PY - 1972
PB - Wolters-Noordhoff Publishing
VL - 24
IS - 2
SP - 129
EP - 174
LA - eng
UR -
ER -


  1. F. Bruhat AND J. Tits[B-T] Groupes algébriques semi-simple sur un corps local, To appear in Publ. I.H.E.S. 
  2. P. Deligne AND D. Mumford[D-M] The irreducibility of the space of curves of given genus. Publ. I.H.E.S.36 (1969) 75-109. Zbl0181.48803MR262240
  3. A. Grothendieck AND J. Dieudonné [EGA] Eléments de la geométrie algébrique, Publ. I.H.E.S., 4, 8, 11, etc. Zbl0118.36206
  4. H. Grauert AND R. Remmert[G-R] Forthcoming book on the foundations of global p-adic function theory. 
  5. Y. Ihara [I] On discrete subgroups of the 2 x 2 projective linear group over p-adic fields, J. Math. Soc. Japan18 (1966) 219-235. Zbl0158.27702MR223463
  6. S. Lichtenbaum [L] Curves over discrete valuation rings, Amer. J. Math.90 (1968) 380-000. Zbl0194.22101MR230724
  7. D. Mumford [M1] Abelian varieties, Oxford Univ. Press, 1970. Zbl0223.14022MR282985
  8. B. Maskit [Ma] A characterization of Schottky groups, J. d'Analyse19 (1967) 227-230. Zbl0168.06201MR220929
  9. J. Mccabe [Mc] Harvard Univ. thesis on P-adic theta functions, (1968) unpublished. 
  10. H. Morikawa [Mo] Theta functions and abelian varieties over valuation rings, Nagoya Math. J.20 (1962). M. Raynaud Zbl0115.39001MR141669
  11. [R] Modèles de Néron, C.R. Acad. Sci., Paris262 (1966) 413-414. J.-P. Serre[S] Groupes Discrets, Mimeo. notes from course at College de France, 1968-69. MR194421
  12. I. Šafarevitch[Š] Lectures on minimal models, Tata Institute Lecture Notes, Bombay, 1966. 

Citations in EuDML Documents

  1. Jeremy Teitelbaum, Geometry of an étale covering of the p -adic upper half plane
  2. David Gieseker, Stable vector bundles and the frobenius morphism
  3. Pierre Jarraud, Jacobiennes des courbes de Mumford
  4. Siegfried Bosch, Stable reduction and rigid analytic uniformization of abelian varieties
  5. Benoît Stroh, Compactification de variétés de Siegel aux places de mauvaise réduction
  6. Yakov Varshavsky, p -adic uniformization of unitary Shimura varieties
  7. Thomas Zink, Über die schlechte Reduktion einiger Shimuramannigfaltigkeiten
  8. Michel Raynaud, Construction analytique de courbes en géométrie non archimédienne
  9. Michel Raynaud, Sections des fibrés vectoriels sur une courbe
  10. Takashi Ichikawa, The universal periods of curves and the Schottky problem

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