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.



Families of ordinary Siegel Modular Forms
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:


* For ordinary families appearing in Betti cohomology, see [Tilouine--Urban, "Several-variable $p$-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations"](http://eudml.org/doc/82495), Ann Sci ENS, 1999.
* For non-ordinary families appearing in functions on a compact form of $Sp(4)$, try the [PhD thesis of Daniel Snaith](http://wwwf.imperial.ac.uk/~buzzard/maths/research/notes/sp2n.pdf) (aka "Caribou"), (Imperial College, early 2000's).
* For a coherent-cohomology approach, more in the style of Coleman's work for $GL(2)$, try [Andrei Jorza's thesis](http://www3.nd.edu/~ajorza/papers/thesis-20100428.pdf) (Princeton, 2010), or for rather stronger results [Andreatta--Iovita--Pilloni](http://annals.math.princeton.edu/2015/181-2/p05) (Annals, this year).


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 $Sp(4)$.


