Lubin-Tate formal groups and module structure over Hopf orders

Werner Bley; Robert Boltje

Journal de théorie des nombres de Bordeaux (1999)

  • Volume: 11, Issue: 2, page 269-305
  • ISSN: 1246-7405

Abstract

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Over the last years Hopf orders have played an important role in the study of integral module structures arising in arithmetic geometry in various situations. We axiomatize these situations and discuss the properties of the (integral) Hopf algebra structures which are of interest in this general setting. In particular, we emphasize the role of resolvents for explicit computations. As an illustration we apply our results to determine the Hopf module structure of the ring of integers in relative Lubin-Tate extensions.

How to cite

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Bley, Werner, and Boltje, Robert. "Lubin-Tate formal groups and module structure over Hopf orders." Journal de théorie des nombres de Bordeaux 11.2 (1999): 269-305. <http://eudml.org/doc/248329>.

@article{Bley1999,
abstract = {Over the last years Hopf orders have played an important role in the study of integral module structures arising in arithmetic geometry in various situations. We axiomatize these situations and discuss the properties of the (integral) Hopf algebra structures which are of interest in this general setting. In particular, we emphasize the role of resolvents for explicit computations. As an illustration we apply our results to determine the Hopf module structure of the ring of integers in relative Lubin-Tate extensions.},
author = {Bley, Werner, Boltje, Robert},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Hopf orders; formal groups; descent; associated orders},
language = {eng},
number = {2},
pages = {269-305},
publisher = {Université Bordeaux I},
title = {Lubin-Tate formal groups and module structure over Hopf orders},
url = {http://eudml.org/doc/248329},
volume = {11},
year = {1999},
}

TY - JOUR
AU - Bley, Werner
AU - Boltje, Robert
TI - Lubin-Tate formal groups and module structure over Hopf orders
JO - Journal de théorie des nombres de Bordeaux
PY - 1999
PB - Université Bordeaux I
VL - 11
IS - 2
SP - 269
EP - 305
AB - Over the last years Hopf orders have played an important role in the study of integral module structures arising in arithmetic geometry in various situations. We axiomatize these situations and discuss the properties of the (integral) Hopf algebra structures which are of interest in this general setting. In particular, we emphasize the role of resolvents for explicit computations. As an illustration we apply our results to determine the Hopf module structure of the ring of integers in relative Lubin-Tate extensions.
LA - eng
KW - Hopf orders; formal groups; descent; associated orders
UR - http://eudml.org/doc/248329
ER -

References

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  2. [B] W. Bley, Elliptic curves and module structure over Hopf orders and The conjecture of Chinburg-Stark for abelian extensions of a quadratic imaginary field. Habilitation Thesis Universität Augsburg, Report des Instituts für Mathematik der Universität Augsburg No. 396, 1998. 
  3. [BT] N. Byott, M.J. Taylor, Hopf orders and Galois module structure. In: Group rings and class groups, R. W. Roggenkamp, M. J. Taylor (eds.) Birkhäuser, BaselBoston, 1992. Zbl0811.11068MR1167451
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  9. [CH] L.N. Childs, S. Hurley, Tameness and local normal bases for objects of finite Hopf algebras. Trans. Amer. Math. Soc.298 (1986), 763-778. Zbl0609.16005MR860392
  10. [dS] E. deShalit, Iwasawa Theory of Elliptic Curves with Complex Multiplication. Perspectives in Math. Vol. 3, Academic Press, 1987. Zbl0674.12004MR917944
  11. [R] I. Reiner, Maximal orders., Academic Press, 1975. Zbl0305.16001MR1972204
  12. [S] R. Schertz, Galoismodulstruktur und Elliptische Funktionen. J. Number Theory39 (1991), 285-326. Zbl0739.11052MR1133558
  13. [ST] A. Srivastav, M.J. Taylor, Elliptic curves with complez multiplication and Galois module structure. Invent. Math.99 (1990), 165-184. Zbl0705.14031MR1029394
  14. [T1] M.J. Taylor, Hopf Structure and the Kummer Theory of Formal Groups. J. Reine Angew. Math.375/376 (1987), 1-11. Zbl0609.12015MR882287
  15. [T2] M.J. Taylor, Mordell-Weil Groups and the Galois Module Structure of Rings of Integers. Illinois J. Math.32 (1988), 428-452. Zbl0631.14033MR947037

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