 Ramification groups of the splitting field of Xp minus p over the p-adic numbers

ID: ramification-groups-of-the-splitting-field-of-xp-minus-p-over-the-p-adic-numbers

For odd

p

K = Q_{p} (ζ_{p}, p p)

is totally ramified of degree

p (p - 1)

. With

ϖ = \frac{ζ _{p} - 1}{p p},

G_{0} = Gal (K / Q_{p}), G_{i} ≅ Z / p Z (1 \leq i \leq p), G_{i} = 1 (i \geq p + 1) .

 New to topics? Read the docs here!