We prove a relative GAGA theorem for perfect and pseudo-coherent complexes in non-archimedean analytic geometry, allowing bases given by Fredholm analytic rings, including those associated from affinoid perfectoid spaces. This answers a question raised in \cite{ heuer2024padicnonabelianhodgetheory}. As an application, we show that for a proper scheme \(X\) and an Artin stack \(Y\) with suitable conditions, the analytification of the algebraic mapping stack \(\mathrm{ Map}(X,Y)\) agrees with the intrinsic analytic mapping stack \(\mathrm{ Map}(X^{ \mathrm{ an}},Y^{ \mathrm{ an}})\).
Categories: math.AG