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We discuss the action of the motivic Hopf element $\\eta$ on this ring, obtain a description of the localization away from $2$ and compute the $2$-primary torsion sub","authors_text":"Egor Zolotarev","cross_cats":["math.AG","math.KT"],"headline":"The P1-diagonal of the homotopy groups of special linear algebraic cobordism equals the special unitary cobordism ring after inverting 2 and the exponential characteristic.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-09-25T14:20:03Z","title":"The geometric diagonal of the special linear algebraic cobordism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16962","kind":"arxiv","version":4},"verdict":{"created_at":"2026-05-23T20:28:05.618567Z","id":"6880cd35-3584-46d7-b99c-96361d853ef7","model_set":{"reader":"grok-4.3"},"one_line_summary":"Computes the P1-diagonal of π_{2*,*}(MSL) over local Dedekind domains (with 1/2 in k, after inverting exp char) and expresses it in terms of the special unitary cobordism ring, along with related characteristic numbers and a motivic Anderson-Brown-Peterson theorem.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The P1-diagonal of the homotopy groups of special linear algebraic cobordism equals the special unitary cobordism ring after inverting 2 and the exponential characteristic.","strongest_claim":"Using this connection, we compute the P1-diagonal of the homotopy groups of the special linear algebraic cobordism π_{2*,*}(MSL) over a local Dedekind domain k with 1/2∈k after inverting the exponential characteristic of the residue field of k. 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