Quotient fields of the perfectoid Tate algebra T_n,K^perfd are semi-immediate extensions of K_r1..rl^perfd with l bounded by min(n-ht(m^flat cap coperf),n-1) and at least one ri irrational if the flat intersection is nonzero.
On torsion in the cohomology of locally symmetric varieties.Ann
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Abhyankar valuations, Pr\"ufer-Manis valuations, and perfectoid Tate algebras
Quotient fields of the perfectoid Tate algebra T_n,K^perfd are semi-immediate extensions of K_r1..rl^perfd with l bounded by min(n-ht(m^flat cap coperf),n-1) and at least one ri irrational if the flat intersection is nonzero.