A geometric description of the class invariant homomorphism

A. Agboola

Journal de théorie des nombres de Bordeaux (1994)

  • Volume: 6, Issue: 2, page 273-280
  • ISSN: 1246-7405

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Agboola, A.. "A geometric description of the class invariant homomorphism." Journal de théorie des nombres de Bordeaux 6.2 (1994): 273-280. <http://eudml.org/doc/93604>.

@article{Agboola1994,
author = {Agboola, A.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {group scheme; Picard invariant homomorphism; Neron model; good reduction; Cartier dual; Kummer order; Kummer extension},
language = {eng},
number = {2},
pages = {273-280},
publisher = {Université Bordeaux I},
title = {A geometric description of the class invariant homomorphism},
url = {http://eudml.org/doc/93604},
volume = {6},
year = {1994},
}

TY - JOUR
AU - Agboola, A.
TI - A geometric description of the class invariant homomorphism
JO - Journal de théorie des nombres de Bordeaux
PY - 1994
PB - Université Bordeaux I
VL - 6
IS - 2
SP - 273
EP - 280
LA - eng
KW - group scheme; Picard invariant homomorphism; Neron model; good reduction; Cartier dual; Kummer order; Kummer extension
UR - http://eudml.org/doc/93604
ER -

References

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  1. [A1] A. Agboola, Iwasawa theory of elliptic curves and Galois module structure, Duke Math. J.71 (1973), 441-462. Zbl0802.11051MR1233444
  2. [A2] A. Agboola, p-adic representations and Galois module structure, preprint. 
  3. [A3] A. Agboola, Abelian varieties and Galois module structure in global function fields, Math. Z. (to appear). Zbl0863.11078
  4. [A4] A. Agboola, On p-adic height pairings and locally free classgroups of Hopf orders, in preparation. Zbl0967.11046
  5. [AT] A. Agboola, M.J. Taylor, Class invariants of Mordell-Weil groups, J. reine angew. Math.447 (1994), 23-61. Zbl0799.11049MR1263168
  6. [BT] N.P. Byott, M.J. Taylor, Hopf orders and Galois module structure, in: Group rings and classgroups, K. W. Roggenkamp, M. J. Taylor (eds.), Birkhauser, 1992. Zbl0811.11068MR1167451
  7. [CM] L. Childs, A. Magid, The Picard invariant of a principal homogeneous space, J. Pure and Appl. Alg.4 (1974), 273-286. Zbl0282.14015MR340266
  8. [CS] G. Cornell, J. Silverman (eds.), Arithmetic Geometry, Springer, 1986. Zbl0596.00007MR861969
  9. [F] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpen, Invent. Math.73 (1983), 349-366. Zbl0588.14026MR718935
  10. [G] R. Greenberg, Iwasawa theory for p-adic representations, Advanced Studies in Pure Mathematics17 (1989), Academic Press, 97-137. Zbl0739.11045MR1097613
  11. [Mi] J. Milne, Abelian varieties, in: Arithmetic Geometry, G. Cornell, J. Silverman (eds.), Springer, 1986. Zbl0604.14028MR861974
  12. [Mu] D. Mumford, Abelian Varieties, OUP, 1970. MR282985
  13. [PR] B. Perrin-Riou, Théorie d'Iwasawa et hauteurs p-adique, Invent. Math.109 (1992), 137-185. Zbl0781.14013MR1168369
  14. [P] A. Plater, Height Pairings on Elliptic Curves, Ph.D. Thesis, Cambridge University, 1991. 
  15. [R] K. Ribet, Kummer theory on extensions of abelian varieties by tori, Duke Math. J.49 (1979), 745-761. Zbl0428.14018MR552524
  16. [Sc] P. Schneider, Iwasawa theory for abelian varieties—a first approach, Invent. Math.71 (1983), 251-293. Zbl0511.14010MR689645
  17. [Se] J.-P. Serre, Algebraic Groups and Class Fields, Springer, 1988. Zbl0703.14001MR918564
  18. [ST] A. Srivastav, M.J. Taylor, Elliptic curves with complex multiplication and Galois module structure, Invent. Math.99 (1990), 165-184. Zbl0705.14031MR1029394
  19. [T1] M.J. Taylor, Mordell-Weil groups and the Galois module structure of rings of integers, Ill. J. Math.32 (1988), 428-452. Zbl0631.14033MR947037
  20. [W] W. Waterhouse, Principal homogeneous spaces and group scheme extensions, AMS Transactions153 (1971), 181-189. Zbl0208.48401MR269659

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