Problem dossier · Algebra
Birch–Tate conjecture
For a totally real number field F, the order of the tame kernel K₂(O_F) equals |w₂(F) · ζ_F(−1)| — K-theory measured by a zeta value.
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Status
Proved for abelian fields up to (and now including most of) the 2-part via Iwasawa theory (Mazur–Wiles, Wiles, Kolster); open in general.
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The Angle of Attack
Verify numerically for small non-abelian totally real fields: compute ζ_F(−1) exactly and bound K₂(O_F) computationally; catalog the 2-torsion behavior.
Tags: k-theory · zeta functions · number fields · iwasawa
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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