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A q-Operator Model for Cyclotomic Syntomic Tate Twists

Author: Wei Yang · Added: July 14, 2026

Article date: July 2026.

Abstract

Let $p$ be an odd prime and $R=\mathbb{Z}_p[\zeta_p]$ . We identify $\mathbb{Z}_p(i)(R)$ , for $i \geq 1$ , with the total fiber of an explicit commuting square of $q$ -operators on $A=\mathbb{Z}_p[[q-1]]$ . The comparison applies Liu’s one-correspondence construction to the defining Nygaard pullback and removes the Hodge-completed derived de Rham term by octahedral cancellation. A finite Herr reduction and an integral cyclotomic residue then compute the cohomology without using the syntomic-etale comparison.