Czechoslovak Mathematical Journal, Vol. 73, No. 4, pp. 1333-1347, 2023
A twisted class number formula and Gross's special units over an imaginary quadratic field
Saad El Boukhari
Received February 10, 2023. Published online November 7, 2023.
Abstract: Let $F/k$ be a finite abelian extension of number fields with $k$ imaginary quadratic. Let $O_F$ be the ring of integers of $F$ and $n\geq2$ a rational integer. We construct a submodule in the higher odd-degree algebraic $K$-groups of $O_F$ 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 $K_{2n-2}(O_F)$.
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