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A twisted class number formula and Gross’s special units over an imaginary quadratic field

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Abstract

Let F/k be a finite abelian extension of number fields with k imaginary quadratic. Let OF be the ring of integers of F and n ⩾ 2 a rational integer. We construct a submodule in the higher odd-degree algebraic K-groups of OF using corresponding Gross’s special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher “twisted” class number of F, which is the cardinal of the finite algebraic K-group K2n−2(OF).

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Authors and Affiliations

  1. Moulay Ismail University, Marjane 2, BP: 298, Meknès, 50050, Morocco

    Saad El Boukhari

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  1. Saad El Boukhari
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El Boukhari, S. A twisted class number formula and Gross’s special units over an imaginary quadratic field. Czech Math J 73, 1333–1347 (2023). https://doi.org/10.21136/CMJ.2023.0067-23

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  • DOI: https://doi.org/10.21136/CMJ.2023.0067-23

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