Pith Number

pith:APTUIGBO

pith:2026:APTUIGBO7XYBCSKMGVUU464CMJ

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Equivariant Hochschild cohomology of group algebras and relative $\operatorname{Ext}$

Andrada Pojar, Constantin-Cosmin Todea

The Γ-equivariant Hochschild cohomology of Γ-algebras equals a kΓ-relative Ext group for any field k.

arxiv:2605.10733 v2 · 2026-05-11 · math.KT

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\pithnumber{APTUIGBO7XYBCSKMGVUU464CMJ}

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Record completeness

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For any field k we show that the Γ-equivariant Hochschild cohomology of Γ-algebras with coefficients in a Γ-equivariant bimodule (Jensen, 1996) is isomorphic with some kΓ-relative Ext, in the context of relative homological algebra.

C2weakest assumption

The groups Γ and G are finite, the action of Γ on G is given, and for the non-triviality conditions the characteristic p of k divides the order of G, with Γ₀ the stabilizer of an element in G.

C3one line summary

Necessary conditions are derived for non-trivial first Γ₀-equivariant Hochschild cohomology of kG, and Γ-equivariant Hochschild cohomology is shown isomorphic to kΓ-relative Ext.

Receipt and verification

First computed	2026-05-21T02:05:05.159534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03e744182efdf011494c35694e7b8262779a0bce0c9254c8d05f091ded4f12d3

Aliases

arxiv: 2605.10733 · arxiv_version: 2605.10733v2 · doi: 10.48550/arxiv.2605.10733 · pith_short_12: APTUIGBO7XYB · pith_short_16: APTUIGBO7XYBCSKM · pith_short_8: APTUIGBO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/APTUIGBO7XYBCSKMGVUU464CMJ \
  | 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: 03e744182efdf011494c35694e7b8262779a0bce0c9254c8d05f091ded4f12d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8734e9dd1a8d25ebce11cfbe7bff46cf150dcfdaeaf2b54b0d952106aaf1d62b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2026-05-11T15:38:05Z",
    "title_canon_sha256": "7fa48b4d7d30310da8be2cdb4f0a42f4600986400fc39d2c021eedc807111f1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10733",
    "kind": "arxiv",
    "version": 2
  }
}