## STNB2019 (33rd edition)

### Integral Hopf Galois structures of degree 2p dihedral extensions

Daniel Gil

#### Abstract

Classical Galois module theory seeks to study the structure of the valuation ring $S$ of an extension $L/K$ of p-adic fields as module over its associated order in the $K$-group algebra of its Galois group $G$. The introduction of Hopf Galois theory allows us to introduce the notion of associated order in an arbitrary Hopf Galois structure of the extension $L/K$, giving rise to the so called Hopf Galois module theory. We present several conditions for the freeness of $S$ over its associated order and study the case of dihedral degree $2p$ extensions of $p$-adic fields. This is a joint work with Anna Rio Doval.