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Bounds For Étale Capitulation Kernels II

Mohsen Asghari-Larimi[1]; Abbas Movahhedi[1]

  • [1] XLIM UMR 6172 CNRS Mathématiques et informatique Université de Limoges 123, Avenue A. Thomas 87060 Limoges Cedex France

Annales mathématiques Blaise Pascal (2009)

  • Volume: 16, Issue: 1, page 151-163
  • ISSN: 1259-1734

Abstract

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Let p be an odd prime and E / F a cyclic p -extension of number fields. We give a lower bound for the order of the kernel and cokernel of the natural extension map between the even étale K -groups of the ring of S -integers of E / F , where S is a finite set of primes containing those which are p -adic.

How to cite

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Asghari-Larimi, Mohsen, and Movahhedi, Abbas. "Bounds For Étale Capitulation Kernels II." Annales mathématiques Blaise Pascal 16.1 (2009): 151-163. <http://eudml.org/doc/10567>.

@article{Asghari2009,
abstract = {Let $p$ be an odd prime and $E/F$ a cyclic $p$-extension of number fields. We give a lower bound for the order of the kernel and cokernel of the natural extension map between the even étale $K$-groups of the ring of $S$-integers of $E/F$, where $S$ is a finite set of primes containing those which are $p$-adic.},
affiliation = {XLIM UMR 6172 CNRS Mathématiques et informatique Université de Limoges 123, Avenue A. Thomas 87060 Limoges Cedex France; XLIM UMR 6172 CNRS Mathématiques et informatique Université de Limoges 123, Avenue A. Thomas 87060 Limoges Cedex France},
author = {Asghari-Larimi, Mohsen, Movahhedi, Abbas},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Capitulation; Tate kernel; K-group; Étale cohomology; capitulation; -group; étale cohomology},
language = {eng},
month = {1},
number = {1},
pages = {151-163},
publisher = {Annales mathématiques Blaise Pascal},
title = {Bounds For Étale Capitulation Kernels II},
url = {http://eudml.org/doc/10567},
volume = {16},
year = {2009},
}

TY - JOUR
AU - Asghari-Larimi, Mohsen
AU - Movahhedi, Abbas
TI - Bounds For Étale Capitulation Kernels II
JO - Annales mathématiques Blaise Pascal
DA - 2009/1//
PB - Annales mathématiques Blaise Pascal
VL - 16
IS - 1
SP - 151
EP - 163
AB - Let $p$ be an odd prime and $E/F$ a cyclic $p$-extension of number fields. We give a lower bound for the order of the kernel and cokernel of the natural extension map between the even étale $K$-groups of the ring of $S$-integers of $E/F$, where $S$ is a finite set of primes containing those which are $p$-adic.
LA - eng
KW - Capitulation; Tate kernel; K-group; Étale cohomology; capitulation; -group; étale cohomology
UR - http://eudml.org/doc/10567
ER -

References

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  10. A. Movahhedi, Sur les p -extensions des corps p -rationnels, (1988) Zbl0723.11054
  11. A. Movahhedi, Sur les p -extensions des corps p -rationnels, Math. Nachr. 149 (1990), 163-176 Zbl0723.11054MR1124802
  12. A. Movahhedi, T. Nguyễ-Quang-Ḏỗ, Sur l’arithmétique des corps de nombres p -rationnels, Séminaire de Théorie des Nombres, Paris 1987–88 81 (1990), 155-200, Birkhäuser Boston, Boston, MA Zbl0703.11059
  13. C. Soulé, K -théorie des anneaux d’entiers de corps de nombres et cohomologie étale, Invent. Math. 55 (1979), 251-295 Zbl0437.12008MR553999
  14. John Tate, Relations between K 2 and Galois cohomology, Invent. Math. 36 (1976), 257-274 Zbl0359.12011MR429837
  15. D Vauclair, Capitulation, Cup-produit et sous-modules finis dans les Z p -extensions d’un corps de nombres, (2005) 

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