Galois scaffolds and Galois module structure for totally ramified C_p²-extensions in characteristic 0

Recently, much work has been done to investigate Galois module structure of local field extensions, particularly through the use of Galois scaffolds. Given a totally ramified p-extension of local fields L/K, a Galois scaffold gives us a K-basis for K[G] whose effect on the valuation of elements of L is easy to determine. In 2013, N.P. Byott and G.G. Elder gave sufficient conditions for the existence of Galois scaffolds for cyclic extensions of degree p² in characteristic p. We take their work and adapt it to cyclic extensions of degree p² in characteristic 0.