Non-Archimedean Analysis

P-adic Banach spaces and families of modular forms

“…Let K be either C p or a complete discretely valued subfield of C p and | | be the absolute value on K such that |p| = p −1 (or more generally we may suppose that K is a complete stable valued field (see [BGR,§3.6.1, Def. 1])).…”

On the closed subfields of Q¯~p${\tilde{\bar Q}}_p$

“…N v/ give distinct restrictions to L and therefore independent. By using a similar argument to that in [6], namely Proposition 1, page 141 from [8], it follows that the completion of L with respect to w (that is a subring of R) is not an integral domain.…”

Maximality of hyperspecial compact subgroups avoiding Bruhat–Tits theory

“…(1) G is affine and smooth over S; (2) for all s ∈ S, thes-algebraic group Gs := G × Ss is connected and reductive (resp. connected and semi-simple).…”