Notes on talk 1. anabelian geometry: introduction
This person is lazy, nothing was left behind...
1. What is contained in “Galois type” data?Gauss: The regular $n$-gon can be constructed by straightedge and compass if and only if $n = 2^{k}p_{1} . . . p_{r}$ where $p_{i} = 2^{2^{n_{i}}} + 1$ are Fermat primes. For example, $n = 17$. (Based on the study of the extension $\mathbb{Q}(\xi_{n})/\mathbb{Q}$ and cyclotomic polynomials). Here the key is that the hidden symmetries are in the Galois group action (not in the geometric symmetry). Later we will consider the “hidden” structures in the abs ...