Structure of central torsion Iwasawa modules

Susan Howson

Bulletin de la Société Mathématique de France (2002)

  • Volume: 130, Issue: 4, page 507-535
  • ISSN: 0037-9484

Abstract

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We describe an approach to determining, up to pseudoisomorphism, the structure of a central-torsion module over the Iwasawa algebra of a pro- p , p -adic, Lie group containing no element of order p . The techniques employed follow classical methods used in the commutative case, but using Ore’s method of localisation. We then consider the properties of certain invariants which may prove useful in determining the structure of a module. Finally, we describe the case of pro- p subgroups of GL 2 ( ℤ p ) in detail and give a brief example from the theory of elliptic curves.

How to cite

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Howson, Susan. "Structure of central torsion Iwasawa modules." Bulletin de la Société Mathématique de France 130.4 (2002): 507-535. <http://eudml.org/doc/272306>.

@article{Howson2002,
abstract = {We describe an approach to determining, up to pseudoisomorphism, the structure of a central-torsion module over the Iwasawa algebra of a pro-$p$, $p$-adic, Lie group containing no element of order $p$. The techniques employed follow classical methods used in the commutative case, but using Ore’s method of localisation. We then consider the properties of certain invariants which may prove useful in determining the structure of a module. Finally, we describe the case of pro-$p$ subgroups of $\mathrm \{GL\}_2 (\mathbb \{Z\}_p) $ in detail and give a brief example from the theory of elliptic curves.},
author = {Howson, Susan},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Iwasawa theory; Euler characteristics; Iwasawa modules; structure theory},
language = {eng},
number = {4},
pages = {507-535},
publisher = {Société mathématique de France},
title = {Structure of central torsion Iwasawa modules},
url = {http://eudml.org/doc/272306},
volume = {130},
year = {2002},
}

TY - JOUR
AU - Howson, Susan
TI - Structure of central torsion Iwasawa modules
JO - Bulletin de la Société Mathématique de France
PY - 2002
PB - Société mathématique de France
VL - 130
IS - 4
SP - 507
EP - 535
AB - We describe an approach to determining, up to pseudoisomorphism, the structure of a central-torsion module over the Iwasawa algebra of a pro-$p$, $p$-adic, Lie group containing no element of order $p$. The techniques employed follow classical methods used in the commutative case, but using Ore’s method of localisation. We then consider the properties of certain invariants which may prove useful in determining the structure of a module. Finally, we describe the case of pro-$p$ subgroups of $\mathrm {GL}_2 (\mathbb {Z}_p) $ in detail and give a brief example from the theory of elliptic curves.
LA - eng
KW - Iwasawa theory; Euler characteristics; Iwasawa modules; structure theory
UR - http://eudml.org/doc/272306
ER -

References

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