Truncated Euler systems. (English) Zbl 1204.11170

Seo, Soogil

J. Reine Angew. Math. 614, 53-71 (2008).

Summary: It is known that the order of the class group \(Cl_{K}\) of the real abelian field \(K\) is essentially equal to the order of the quotient \(E_{K}/C_{K}\) of the global units \(E_{K}\) by the circular units \(C_{K}\) of \(K\). However, the structures of these two groups are usually very different. Motivated by the theory of circular distributions and the special units of Rubin, we introduce a filtration to \(E_{K}\) made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We use Euler systems to give evidence for this conjecture.

MSC:

11R23	Iwasawa theory
11G16	Elliptic and modular units
11R27	Units and factorization
11R29	Class numbers, class groups, discriminants

References:

[1]	Coleman R., Math. 356 pp 161– (1985)
[2]	Greither C., Ann. Inst. Fourier (Grenoble) 42 pp 449– (1992)
[3]	DOI: 10.1007/BF01388983 · Zbl 0628.12007 · doi:10.1007/BF01388983
[4]	DOI: 10.1006/jnth.2000.2634 · Zbl 0995.11060 · doi:10.1006/jnth.2000.2634
[5]	DOI: 10.1023/A:1023644822410 · Zbl 1023.11056 · doi:10.1023/A:1023644822410
[6]	DOI: 10.1016/j.jnt.2004.06.010 · Zbl 1081.11070 · doi:10.1016/j.jnt.2004.06.010
[7]	Seo S., Math. Res. Let. 13 pp 1– (2006)
[8]	DOI: 10.2307/1970932 · Zbl 0395.12014 · doi:10.2307/1970932
[9]	DOI: 10.1007/BF01389158 · Zbl 0465.12001 · doi:10.1007/BF01389158
[10]	DOI: 10.1017/S0305004100069073 · Zbl 0717.11046 · doi:10.1017/S0305004100069073