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Refined class number formulas for elliptic units

Refined class number formulas for elliptic units We generalize the notions of Kolyvagin and pre-Kolyvagin systems to prove “refined class number formulas” for quadratic extensions of a quadratic imaginary fields $$K$$ K of class number one. Our main result generalises the results and conjectures of Darmon (Canad. J. Math. 47:302–317, 1995), by replacing circular units in abelian extensions of $$\mathbb {Q}$$ Q by elliptic units in abelian extensions of K. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales mathématiques du Québec Springer Journals

Refined class number formulas for elliptic units

Gomez, C.
Annales mathématiques du Québec , Volume 39 (1) – Dec 19, 2014
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24 pages

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Fondation Carl-Herz and Springer International Publishing Switzerland
Subject
Mathematics; Mathematics, general; Number Theory; Algebra; Analysis
ISSN
2195-4755
eISSN
2195-4763
DOI
10.1007/s40316-014-0023-1
Publisher site
See Article on Publisher Site

Abstract

We generalize the notions of Kolyvagin and pre-Kolyvagin systems to prove “refined class number formulas” for quadratic extensions of a quadratic imaginary fields $$K$$ K of class number one. Our main result generalises the results and conjectures of Darmon (Canad. J. Math. 47:302–317, 1995), by replacing circular units in abelian extensions of $$\mathbb {Q}$$ Q by elliptic units in abelian extensions of K.

Journal

Annales mathématiques du Québec – Springer Journals

Published: Dec 19, 2014

References

  • Thaine’s method for circular units and a conjecture of Gross
    Darmon, H
  • Refined class number formulas and Kolyvagin systems
    Mazur, B; Rubin, K
  • Refined conjectures of the Birch and Swinnerton-Dyer type
    Mazur, B; Tate, J