Twisted Lubin-Tate Big Witt Vectors and Fleck-Sun-Wan Congruences

Abstract

We construct a big Witt theory associated with coefficient-multiplicative normalized $\sigma$-twisted Lubin-Tate formal groups. The resulting $F$-big Witt ring extends Hazewinkel's ramified $q$-typical Witt theory and recovers the usual big Witt ring in the multiplicative case. We also introduce Fleck operators defined from iterated Coleman traces and prove Lubin-Tate analogues of the Fleck-Sun-Wan congruences for both positive and negative powers. By relating the Lubin-Tate Coleman theory to the $F$-big Witt theory, we obtain a Coleman $F$-norm whose integrality yields congruences among the corresponding Fleck coefficients.