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

El Boukhari, Saad

Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1333-1347

Abstract (VO)

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 $n\geq 2$ 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 $K_{2n-2}(O_F)$.

Détail

DOI : 10.21136/CMJ.2023.0067-23

Classification : 11R70, 19F27
Keywords: algebraic $K$-theory; Dedekind zeta function; Artin $L$-function; Beilinson regulator; generalized index; Lichtenbaum conjecture

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