Pith Number

pith:JI775NO2

pith:2026:JI775NO2HQCKH4B2SWXRBHJ3SA

not attested not anchored not stored refs resolved

The Localization Theorem for the Motivic Homotopy Theory of Complex Analytic Stacks and other Geometric Settings

Roy Magen

The localization theorem of Morel and Voevodsky holds for motivic homotopy theory over complex analytic stacks.

arxiv:2605.14470 v1 · 2026-05-14 · math.AG · math.CT

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JI775NO2HQCKH4B2SWXRBHJ3SA}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

We prove the analog of the Morel-Voevodsky localization theorem over complex analytic stacks, which is used in arXiv:2511.09371 to establish a 6-functor formalism of complex analytic motivic homotopy theory.

C2weakest assumption

The geometric properties of complex analytic stacks (such as the existence of suitable model structures or localization properties) are compatible with the motivic homotopy framework in the same way as in the algebraic case.

C3one line summary

Proves the localization theorem for motivic homotopy theory over complex analytic stacks and supplies general techniques for algebraic and differentiable stacks.

References

36 extracted · 36 resolved · 2 Pith anchors

[1] Jarod Alper , Jack Hall , and David Rydh , The \'e tale local structure of algebraic stacks , arXiv e-prints (2025), arXiv:1912.06162 2025

[2] I , Ast\'erisque (2007), no 2007

[3] II , Ast\'erisque (2007), no 2007

[4] Denis-Charles Cisinski and Frédéric Déglise, Triangulated categories of mixed motives, Springer International Publishing, 2019 2019

[5] thesis, Universit \"a ts-und Landesbibliothek Bonn, 2023 2023

Receipt and verification

First computed	2026-05-17T23:39:06.672383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a3ffeb5da3c04a3f03a95af109d3b902b800f6ddf1336926a2b0d511fe2e7ad

Aliases

arxiv: 2605.14470 · arxiv_version: 2605.14470v1 · doi: 10.48550/arxiv.2605.14470 · pith_short_12: JI775NO2HQCK · pith_short_16: JI775NO2HQCKH4B2 · pith_short_8: JI775NO2

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/JI775NO2HQCKH4B2SWXRBHJ3SA \
  | 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: 4a3ffeb5da3c04a3f03a95af109d3b902b800f6ddf1336926a2b0d511fe2e7ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec2c30639275d75b5e975fa73eb9751cbafeb46abfadf8b887aad041f484f6c0",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-14T07:04:31Z",
    "title_canon_sha256": "0edc446f76e3cad7febad294e965a782eab4a5924291f0f45cd26243ede47ac2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14470",
    "kind": "arxiv",
    "version": 1
  }
}