We extend Greenberg's original construction to arbitrary schemes over (certain types of)
local artinian rings. We then establish a number of properties of the extended functor and …

Let X be a projective, equidimensional, singular scheme over an algebraically closed field.
Then the existence of a geometric smoothing (ie a family of deformations of X over a smooth …

We define a formal algebraic analogue of hypertoric Hitchin systems, whose complex-
analytic counterparts were defined by Hausel–Proudfoot. These are algebraic completely …

We introduce Néron models of formally finite (ff) type for uniformly rigid spaces, thereby
generalizing formal Néron models for rigid-analytic groups as they had been studied by …

We define the cotangent complex of a morphism f: X→ Y of locally noetherian formal
schemes as an object in the derived category D−(X) through local homology. We discuss its …

We provide the main results of a deformation theory of smooth formal schemes as defined in
[L. Alonso Tarrío, A. Jeremías López, M. Pérez Rodríguez, Infinitesimal lifting and Jacobi …

[ES] En la presente memoria se aborda el problema de móduli de G-fibrados principales
sobre una curva algebraica lisa y proyectiva definida sobre un cuerpo K algebraicamente …

Formal schemes are (topologically) ringed spaces that Grothendieck introduced in EGA.
They are simultaneously analogues for admissible rings of schemes for general …

We introduce a new category of non-archimedean analytic spaces over a complete
discretely valued field. These spaces, which we call uniformly rigid, may be viewed as …

In this thesis we develop a Chabauty-Kim theory for the relative completion of motivic
fundamental groups, including Selmer stacks and moduli spaces of admissible torsors for …