Pith Number

pith:TEQNQDXN

pith:2024:TEQNQDXNDJZZ6PE2HBEGTZDHL7

not attested not anchored not stored refs pending

The geometric diagonal of the special linear algebraic cobordism

Egor Zolotarev

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.

arxiv:2409.16962 v4 · 2024-09-25 · math.AT · math.AG · math.KT

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Record completeness

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4 Citations open

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Claims

C1strongest 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. The complete answer is given in terms of the special unitary cobordism ring.

C2weakest assumption

The computation assumes the base ring is a local Dedekind domain containing 1/2 and that the exponential characteristic of the residue field can be inverted without losing the essential structure of the homotopy groups.

C3one 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.

Receipt and verification

First computed	2026-06-03T02:05:40.011617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9920d80eed1a739f3c9a384869e4675fe86d7042c5b850c453dbaea20998234d

Aliases

arxiv: 2409.16962 · arxiv_version: 2409.16962v4 · doi: 10.48550/arxiv.2409.16962 · pith_short_12: TEQNQDXNDJZZ · pith_short_16: TEQNQDXNDJZZ6PE2 · pith_short_8: TEQNQDXN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TEQNQDXNDJZZ6PE2HBEGTZDHL7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9920d80eed1a739f3c9a384869e4675fe86d7042c5b850c453dbaea20998234d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92163698390a80be82b9d2677d989436b1d3fea15311d69352df191a51293ad8",
    "cross_cats_sorted": [
      "math.AG",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2024-09-25T14:20:03Z",
    "title_canon_sha256": "a99c9e273f0f8e2e464f04624c0e5e6c7d0c8babeee1bf7f19ad05fe3297a663"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.16962",
    "kind": "arxiv",
    "version": 4
  }
}