In contrast to scheme theory, it is difficult to construct fundamental theories of rigid geometry such as a theory of quasi-coherent sheaves because of issues of topological algebraic systems such as topological rings and topological modules. Recently Clausen and Scholze have developed a new approach to treat them, which is called condensed mathematics. By using this, we generalize faithfully flat descent of pseudo-coherent complexes on rigid analytic varieties to that of quasi-coherent complexes. In this talk, we will formulate fppf-descent for schemes in the context of condensed mathematics, then by using this we will explain the proof of faithfully flat descent for formal models of rigid analytic varieties, which implies faithfully flat descent for rigid analytic varieties.

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