A Lefschetz principle in non-archimedean geometry
-- Brian Conrad, September 12, 2014

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In analytic geometry over a non-archimedean field it
is often convenient to work over a ground field that is
algebraically closed, but that can create some difficulties
because such fields have non-noetherian valuation ring.  We
explain a technique based on deformation theory and formal
algebraic spaces to reduce certain problems in relative
non-archimedean geometry to the case of a discretely-valued
ground field, and give an application to de Rham cohomology,
answering a question of Scholze.  This is joint work with
O. Gabber.