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Motivic cohomology is a cohomology theory that can be defined internally within Grothendieck's category of motives. Voevodsky developed this theory for smooth varieties, demonstrating its deep connections to algebraic cycles and algebraic K-theory. However, its behaviour in mixed characteristic remains less well understood. Building on recent advances by Bachmann, Elmanto, Morrow, and Bouis, in joint work with Bouis we establish a purity result over deeply ramified bases. I will also discuss an application of this result to p-adic Hodge theory.