Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Unipotent groups associated to reduced curves

Author: David Penniston
Journal: Trans. Amer. Math. Soc. 352 (2000), 5025-5043
MSC (1991): Primary 14H40; Secondary 14L17, 14H20
Published electronically: July 12, 2000
MathSciNet review: 1695033
Full-text PDF

Abstract | References | Similar Articles | Additional Information


Let $X$ be a curve defined over an algebraically closed field $k$ with $\operatorname{char}(k)=p>0$. Assume that $X/k$ is reduced. In this paper we study the unipotent part $U$ of the Jacobian $J_{X/k}$. In particular, we prove that if $p$ is large in terms of the dimension of $U$, then $U$ is isomorphic to a product of additive groups $\mathbb{G} _a$.

References [Enhancements On Off] (What's this?)

  • [Bom] E. Bombieri, Seminormalità e singolarità ordinarie, Symposia Mathematica XI, Academic Press, New York (1972), 205-210. MR 55:2884
  • [BLR] S. Bosch, W. Lütkebohmert and M. Raynaud, Néron Models, Springer-Verlag, Berlin, Heidelberg, New York (1990). MR 91i:14034
  • [Edi] B. Edixhoven, On the prime-to-$p$ part of the groups of connected components of Néron models, Compositio Math. $\mathbf{97}$ (1995), 29-49. MR 96h:14066
  • [Kat] N. Katz, Galois properties of torsion points on abelian varieties, Invent. Math. $\mathbf{62}$ (1981), 481-502. MR 82d:14025
  • [L-O] H. W. Lenstra, Jr. and F. Oort, Abelian varieties having purely additive reduction, J. Pure Appl. Alg. $\mathbf{36}$(1985), 281-298. MR 86e:14020
  • [Lor] D. Lorenzini, Groups of components of Néron models of Jacobians, Compositio Math. $\mathbf{73}$ (1990), 145-160. MR 92d:14019
  • [Lor2] D. Lorenzini, On the group of components of a Néron model, J. Reine Angew. Math. 445 (1993), 109-160. MR 94k:11065
  • [N-W] A. Nijenhuis and H. Wilf, Representations of integers by linear forms in nonnegative integers, J. Number Theory $\mathbf{4}$ (1972), 98-106. MR 44:5274
  • [Ser] J.-P. Serre, Groupes Algébriques et Corps de Classes, Hermann, Paris (1959). MR 21:1973

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 14H40, 14L17, 14H20

Retrieve articles in all journals with MSC (1991): 14H40, 14L17, 14H20

Additional Information

David Penniston
Affiliation: Department of Mathematics, Pennsylvania State University, 218 McAllister Building, University Park, Pennsylvania 16802
Address at time of publication: Department of Mathematics, Furman University, Greenville, South Carolina 29613

Received by editor(s): September 13, 1998
Received by editor(s) in revised form: March 17, 1999
Published electronically: July 12, 2000
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society