Continuous K-theory of nuclear modules on Spf(R^hat_I) is isomorphic to lim_n K(R/I^n), via internal projectivity and strongly Mittag-Leffler inverse sequences.
Barwick, ``On the algebraic K-theory of higher categories''
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Localizing invariants of inverse limits
Continuous K-theory of nuclear modules on Spf(R^hat_I) is isomorphic to lim_n K(R/I^n), via internal projectivity and strongly Mittag-Leffler inverse sequences.