Groups of components of Néron models of jacobians

Dino J. Lorenzini

Compositio Mathematica (1990)

  • Volume: 73, Issue: 2, page 145-160
  • ISSN: 0010-437X

How to cite


Lorenzini, Dino J.. "Groups of components of Néron models of jacobians." Compositio Mathematica 73.2 (1990): 145-160. <>.

author = {Lorenzini, Dino J.},
journal = {Compositio Mathematica},
keywords = {minimal model; Jacobian variety; Néron model},
language = {eng},
number = {2},
pages = {145-160},
publisher = {Kluwer Academic Publishers},
title = {Groups of components of Néron models of jacobians},
url = {},
volume = {73},
year = {1990},

AU - Lorenzini, Dino J.
TI - Groups of components of Néron models of jacobians
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 73
IS - 2
SP - 145
EP - 160
LA - eng
KW - minimal model; Jacobian variety; Néron model
UR -
ER -


  1. [1] M. Artin and G. Winters, Degenerate fibers and stable reduction of curves. Topology10 (1971), 373-383. Zbl0196.24403MR476756
  2. [2] G. Cornell and J. Silverman, Eds. Arithmetic Geometry. Spinger-Verlag, 1986. Zbl0596.00007MR861969
  3. [3] M. Deschamps, Réduction semi-stable. In Séminaire sur les pinceaux de courbes de genre au moins deux (1981), L. Szpiro, Ed., pp. 1-34. Zbl0505.14008
  4. [4] I. Dolgačev, On the purity of the degeneration loci of families of curves. Invent. Math.8 (1969), 34-54. Zbl0176.18503MR263817
  5. [5] A. Grothendieck, Exposés I and IX in the Séminaire de géométrie algébrique SGA 7 I. Lect. Notes Math. 288, Springer-Verlag, 1970. 
  6. [6] S. Lang, Introduction to Arakelov Theory. Springer-Verlag, 1988. Zbl0667.14001MR969124
  7. [7] H. Lenstra, and F. Oort, Abelian varieties having purely additive reduction. J. Pure and Applied Alg.36 (1985), 281-298. Zbl0557.14022MR790619
  8. [8] J. Lipman, Introduction to resolution of singularities. In Algebraic Geometry, Arcata 1974 (1975), AMS Proc. Symp. Pure Math. 29. Zbl0306.14007MR389901
  9. [9] D. Lorenzini, Arithmetical graphs. To appear in Math. Annalen. Zbl0662.14008MR1019714
  10. [10] D. Lorenzini, Dual graphs of degenerating curves. To appear in Math. Annalen. Zbl0668.14019MR1048284
  11. [11] W McCallum, The component group of a Néron model. Preprint. 
  12. [12] T. Oda and C. Seshadri, Compactification of the generalized jacobian variety. Trans. of AMS253 (1979), 1-90. Zbl0418.14019MR536936
  13. [13] A. Ogg, Elliptic curves and wild ramification. Amer. J. Math.89 (1967), 1-21. Zbl0147.39803MR207694
  14. [14] F. Oort, A construction of generalized jacobians varieties by group extensions. Math. Annalen147 (1962), 277-286. Zbl0101.38502MR141667
  15. [15] F. Oort, Good and stable reduction of abelian varieties. Manuscr. Math.11 (1974), 171-197. Zbl0266.14016MR347834
  16. [16] M. Raynaud, Spécialisation du foncteur de Picard. Publ. Inst. Hautes Etudes Sci., Paris38 (1970), 27-76. Zbl0207.51602MR282993
  17. [17] T. Saito, Vanishing cycles and the geometry of curves over a discrete valuation ring. Amer. J. Math.109 (1987), 1043-1085. Zbl0673.14014MR919003
  18. [18] J.-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Invent. Math.15 (1972), 259-331. Zbl0235.14012MR387283
  19. [19] J.-P. Serre and J. Tate, Good reduction of abelian varieties. Ann. of Math.88 (1968), 492-517. Zbl0172.46101MR236190
  20. [20] J. Silverman, The Néron fiber of abelian varieties with potential good reduction. Math. Annalen264 (1983), 1-3. Zbl0497.14016MR709856
  21. [21] J. Silverman, The Arithmetic of Elliptic Curves. Spinger-Verlag, 1986. Zbl0585.14026MR817210
  22. [22] J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil. In Modular functions in one variable IV (1975), Springer Lect. Notes in Math. vol. 476. Zbl1214.14020MR393039
  23. [23] E. Viehweg, Invarianten der degenerierten Fasem in lokalen Familien von Kurven. J. Reine Math.293 (1977), 284-308. Zbl0349.14017MR498554
  24. [24] G. Winters, On the existence of certain families of curves. Amer. J. Math.96 (1974), 215-228. Zbl0334.14004MR357406

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