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I'm looking for references to constructions and treatments of Hida Families/Eigenvarieties for ordinary Siegel modular forms (In particular: genus 2).

So far I've been reading Richard Taylor's thesis and would like to find more.

Thanks in advance.

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This is a very rich and active subject. There are lots of different approaches to the problem, giving more or less strong results -- you can try to interpolate any or all of { Hecke eigenvalues, Fourier coefficients, L-values, Galois representations }, for forms satisfying various different flavours of finite-slope condition, while the weight varies in families having different numbers of parameters. Here are a selection of the important works on this:

These are just the references I know that treat Siegel modular forms specifically; there are other references that treat general reductive groups from which one can extract something for $Sp(4)$.

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