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Recently, much work has been done to investigate Galois module structure oflocal field extensions, particularly through the use of Galois scaffolds. Givena totally ramified $p$-extension of local fields $L/K$, a Galois Scaffold givesus a $K$-basis for $K[G]$ whose effect on the valuation of elements of $L$ iseasy to determine. In 2013, N.P. Byott and G.G. Elder gave sufficientconditions for the existence of Galois scaffolds for cyclic extensions ofdegree $p^2$ in characteristic $p$. We take their work and adapt it to cyclicextensions of degree $p^2$ in characteristic $0$.

Galois Scaffolds and Galois Module Structure for Totally Ramified $C_p^2$-Extensions in Characteristic 0