A note on cyclotomic Euler systems and the double complex method

Greg W. Anderson, Yi Ouyang

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Let double-struk f sign be a finite real abelian extension of ℚ. Let M be an odd positive integer. For every squarefree positive integer r the prime factors of which are congruent to 1 modulo M and split completely in double-struk f sign, the corresponding Kolyvagin class κr ∈ double-struk f sign× /double-struk f sign ×M satisfies a remarkable and crucial recursion which for each prime number ℓ dividing r determines the order of vanishing of κ r at each place of double-struk f sign above ℓ in terms of κr/ℓ. In this note we give the recursion a new and universal interpretation with the help of the double complex method introduced by Anderson and further developed by Das and Ouyang. Namely, we show that the recursion satisfied by Kolyvagin classes is the specialization of a universal recursion independent of double-struk f sign satisfied by universal Kolyvagin classes in the group cohomology of the universal ordinary distribution à la Kubert tensored with ℤ/Mℤ. Further, we show by a method involving a variant of the diagonal shift operation introduced by Das that certain group cohomology classes belonging (up to sign) to a basis previously constructed by Ouyang also satisfy the universal recursion.

Original languageEnglish (US)
Pages (from-to)673-692
Number of pages20
JournalCanadian Journal of Mathematics
Volume55
Issue number4
DOIs
StatePublished - Aug 2003

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