Algebraization of a Cartier divisor
  We extend to pairs classical results of R. Elkik on lifting of homomorphisms and algebraization. In particular, we establish algebraization of an affine rig-smooth formal variety with a rig-smooth closed subvariety. This solves affirmatively a problem raised by M. Temkin and has applications to desingularization theory. 
Dmitry Trushin
math.AC