Spreading-out of rigid-analytic families and observations on p-adic Hodge theory

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Spreading-out of rigid-analytic families and observations on p-adic Hodge theory
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(Joint work with Brian Conrad.) Let K be a complete rank 1 valued field with ring of integers OK, A an adic noetherian ring and f: A→OK an adic morphism. If g: X→Y is a proper flat morphism between rigid analytic spaces over Kthen locally on Y a flat formal model of gspreads out to a proper flat morphism between formal schemes topologically of finite type over A. As an application one can prove that for proper smooth g and K of characteristic 0, the Hodge to de Rham spectral sequence for g degenerates and the RqgxΩpX/Y are locally free.
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