| Abstract | We present our construction on the local model of Hilbert-Siegel varieties in \Gamma_1(p)-level. This generalizes the previous work in the Siegel case by Haines and Stroh. A key tool used by Haines-Stroh is the cotangent complex. To generalize to the Hilbert-Siegel case, one needs to consider the corresponding equivariant cotangent complex. For this, we define a variant over the Zariski site of the ring-equivariant cotangent complex (or more precisely, the Lie complex) constructed by Illusie in his thesis. In the two talks, we will recall Illusie’s theory and present our new definition, then we explain how our definition is used in the construction of the local model. |
