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- W2401943145 abstract "We present several new examples of reflection principles which apply to both class groups of number fields and picard groups of of curves over $mathbb{P}^{1}/mathbb{F}_{p}$. This proves a conjecture of Lemmermeyer about equality of 2-rank in subfields of $A_{4}$, up to a constant not depending on the discriminant in the number field case, and exactly in the function field case. More generally we prove similar relations for subfields of a Galois extension with group $G$ for the cases when $G$ is $S_{3}$, $S_{4}$, $A_{4}$, $D_{2l}$ and $mathbb{Z}/lmathbb{Z}rtimesmathbb{Z}/rmathbb{Z}$. The method of proof uses sheaf cohomology on 1-dimensional schemes, which reduces to Galois module computations." @default.
- W2401943145 created "2016-06-24" @default.
- W2401943145 creator A5084796787 @default.
- W2401943145 date "2016-05-14" @default.
- W2401943145 modified "2023-09-27" @default.
- W2401943145 title "Reflection principles for class groups" @default.
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