On p-adic families of automorphic forms

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Overconvergent Hilbert modular forms (2005, methodology): “There are other approaches to theorems such as the above, which are based on switching from forms on GL2 /F to forms on definite quaternion algebras and making certain representation theoretic constructions—see for example forthcoming work of Buzzard [Bu1], [Bu2], as well as [Che], [Em] and [Kas] fo”
On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms (2006, methodology): “There is also an approach, the basic idea of which is due to Stevens (generalizing the approach of Hida [20] in the ordinary case), that has been developed by Ash and Stevens (for the group GLn over Q [2]), Buzzard (for tori and for definite quaternion algebras over Q [ 5 ], and for totally definite”
The eigencurve over the boundary of weight space (2014, methodology): “(The reason for our choice is to match with the convention used in Buzzard [Bu04] as shown by (2.”
L -functions and Galois Representations: Eigenvarieties (2007, methodology): “(b) The existence of XΓ is Lemma 2(i) of [5].”
Hida families and rational points on elliptic curves (2007, methodology): “The methods developed in Section 6 of [GS] is sufficient to handle the case of interest in this paper, which is only concerned with Hida families of ordinary eigenforms, and this allows us to work with measures (elements of D†) rather than the locally analytic functions and distributions that appear”