Structure of central torsion Iwasawa modules
Bulletin de la Société Mathématique de France (2002)
- Volume: 130, Issue: 4, page 507-535
- ISSN: 0037-9484
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topHowson, 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
top- [1] J.-E. Björk – « Filtered Noetherian Rings », Noetherian Rings and their Applications, Math. Surv. Monogr., vol. 24, Oberwolfach/FRG, 1983, p. 59–97. Zbl0648.16001MR921079
- [2] M. Boratynsky – « A Change of Rings Theorem and the Artin-Rees Property », Proc. Amer. Math. Soc.53 (1975), p. 307–310. Zbl0319.16024MR401840
- [3] S. Bosch, U. Guntzer & R. Remmert – Non-Archimedean Analysis, Grundlehren der mathematischen Wissenschaften, vol. 261, Springer Verlag, 1984. Zbl0539.14017MR746961
- [4] A. Brumer – « Pseudocompact Algebras, Profinite Groups and Class formations », J. Algebra4 (1966), p. 442–470. Zbl0146.04702MR202790
- [5] J. Coates & S. Howson – « Euler Characteristics and Elliptic Curves II », J. Math. Soc. Japan 53 (2001), no. 1, p. 175–235. Zbl1046.11079MR1800527
- [6] J. Coates & R. Sujatha – « Euler-Poincaré Characteristics of Abelian Varieties », C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 4, p. 309–313. Zbl0967.14029MR1713337
- [7] —, Galois Cohomology of Elliptic Curves, Lecture Notes at the Tata Institute of Fundamental Research, 2000. Zbl0973.11059MR1759312
- [8] J. Coates, R. Sujatha & J.-P. Wintenberger – « On the Euler-Poincaré Characteristics of Finite Dimensional -adic Galois Representations », Publ. Math. IHES93 (2001), p. 107–143. Zbl1143.11021MR1863736
- [9] P. Cohn – Algebra, vol. 1, Wiley, 1993. Zbl0341.00002MR360046
- [10] J. Dixon, M. duSautoy, A. Mann D. Segal – Analytic pro-p groups, 2 éd., Cambridge Studies in Advanced Mathematics, vol. 61, C.U.P., 1999. Zbl0934.20001MR1720368
- [11] Y. Hachimori & K. Matsuno – « An Analogue of Kida’s Formula for the Selmer Group of Elliptic Curves », J. Alg. Geom.8 (1999), p. 581–601. Zbl1081.11508MR1689359
- [12] M. Harris – « -adic Representations Arising from Descent on Abelian Varieties », Compositio Math. 39 (1979), no. 2, p. 177–245. Zbl0417.14034MR546966
- [13] S. Howson – « Euler Characteristics as Invariants of Iwasawa Modules », preprint to appear in Proc. London Math. Soc., 2002. Zbl1036.11053MR1936815
- [14] S. Lang & H. Trotter – Frobenius Distributions in GL-extensions: Distribution of Frobenius automorphisms in GL-extensions of the Rational Numbers, LNM, vol. 504, Springer Verlag, 1976. Zbl0329.12015MR568299
- [15] J. McConnell & J. Robson – Noncommutative Noetherian Rings, Wiley-Interscience, 1987. Zbl0644.16008MR934572
- [16] J. Neukirch, A. Schmidt & K. Wingberg – Cohomology of Number Fields, Grundlehren der mathematischen Wissenschaften, vol. 323, Springer Verlag, 2000. Zbl0948.11001MR1737196
- [17] A. Neumann – « Completed group algebras without zero divisors », Arch. Math.51 (1988), p. 496–499. Zbl0669.16007MR973723
- [18] Y.-H. Ochi & O. Venjakob – « On the Structure of Selmer Groups over -adic Lie Extensions », J. Alg. Geom. 11 (2002), no. 3, p. 547–580. Zbl1041.11041MR1894938
- [19] A. Scholl & R. Taylor (éds.) – Galois Representations in Arithmetic and Geometry, L.M.S., C.U.P., 1998, Papers from the Durham Colloquium, 1996.
- [20] J.-P. Serre – « Sur la dimension cohomologique des groupes profinis », Topology3 (1965), p. 413–420. Zbl0136.27402MR180619
- [21] —, « La distribution d’Euler-Poincaré d’un groupe profini », Galois Representations in Arithmetic and Geometry, 1998, See [19].
- [22] B. Totaro – « Euler Characteristics for -adic Lie Groups », Publ. Math. IHES (1999), p. 169–225. Zbl0971.22011MR1813226
- [23] O. Venjakob – « Dissertation », Thèse, Heidelberg, 2000.
- [24] C. Weibel – An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics, 38, C.U.P., 1994. Zbl0797.18001MR1269324
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