New Results on the Segal Conjecture in p-adic Geometry

This research explores the interplay between de-completed topological periodic cyclic homology, the Segal conjecture, and F-smoothness within the realm of p-adic geometry. The study establishes completeness of motivic filtration and reveals connections to Manam's Frobenius untwisted topological periodic cyclic homology. Furthermore, it leverages cyclotomic synthetic spectra to derive a relative conjugate filtration, ultimately leading to insights into weak and strong F-smoothness.