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Elliptic units and sign functions. (English) Zbl 1161.11356

Summary: In the first part of this paper we give a new definition of the elliptic analogue of Sinnott’s group of circular units. In this we essentially use the ideas discussed in the author’s paper [Ann. Inst. Fourier 55, No. 3, 753–772 (2005; Zbl 1158.11320)]. In the second part of the paper we are interested in computing the index of this group of elliptic units. This question is closely related to the behaviour of the universal signed ordinary distributions introduced in loc. cit. Such distributions have a natural resolution discovered by G. W. Anderson [Recent progress in algebra. Proceedings of an international conference, Contemp. Math. 224, 1–27 (1999; Zbl 0939.11035)]. Consequently, we can apply Y. Ouyang’s general index formula [J. Reine Angew. Math. 537, 1–32 (2001; Zbl 1008.11042)] and the powerful Anderson’s theory of double complex to make the computations

MSC:

11G16 Elliptic and modular units
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