Manfred Kolster - Higher relative class number formulas

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Manfred Kolster - Higher relative class number formulas

MANFRED KOLSTER, Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada

Higher relative class number formulas

Let F/F⁺ be a CM extension of number fields, and let $\chi$ denote the non-trivial character of the Galois group of F/F⁺. The classical relative class number formula gives the following relation between the value of the L-function of $\chi$ at 0 and the relative class number h^-:

$\begin{displaymath}L_{F^+}(\chi,0) = \frac{2^{r_1}}{Q} \cdot \frac{h^-}{w(F)}, \end{displaymath}$

where $r_1 = [F^+:\bbd Q]$ , Q is the so-called Q-index, and w(F)is the number of roots of unity in F. The purpose of the talk is to describe analogs of this formula relating the values $L_{F^+}(\chi, 1-n)$ for $n \geq 3$ an odd integer to the orders of relative motivic cohomology groups and K-groups.

Next: Arne Ledet - Some Up: Number Theory / Théorie Previous: Hershey Kisilevsky - Rank