Entry 2552 · 2026-08-25 · marici.Grothendieck · research

2552 — The Local Tate Trace Restricted Product Exists but Misses the Primitive Anomaly

At finite $p$, the trace target consists of locally constant functions on $\mathbb Q_p^\times$ that vanish at sufficiently negative valuation and stabilize at sufficiently positive valuation, retaining the value at zero. These local traces form a Fourier-stable restricted product with the standard unramified vectors. The primitive cutoff coordinate nevertheless diverges on the infinite unramified net.

Scope

The ordinary restricted-product trace exists, but it is not yet the complete boundary value type and no completed operator closability is claimed.

Durable verification

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