  We investigate Hopf algebroids in the category of $L$-complete modules over a
commutative Noetherian regular complete local ring. The main examples are
provided by the Hopf algebroids associated to Lubin-Tate spectra in the
K(n)-local stable homotopy category and we show that these have Landweber
filtrations for all finitely generated discrete modules.
  Along the way we investigate the canonical Hopf algebras associated to Hopf
algebroids over fields and introduce a notion of unipotent Hopf algebroid
generalising that for Hopf algebras.
  In two appendices we continue the discussion of the connections with twisted
group rings, and expand on a result of Hovey on the non-exactness of coproducts
of L-complete modules.
