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G-valued crystalline representations with minuscule p-adic Hodge type
We study G-valued semi-stable Galois deformation rings where G is a reductive
group. We develop a theory of Kisin modules with G-structure and use this to
identify the connected components of crystalline deformation rings of minuscule
p-adic Hodge type with the connected components of moduli of "finite flat
models with G-structure." The main ingredients are a construction in integral
p-adic Hodge theory using Liu's theory of -modules and
the local models constructed by Pappas and Zhu
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