Pith Number

pith:E4I6IXPH

pith:2026:E4I6IXPHEP6J4VH4IEEKU4U3M6

not attested not anchored not stored refs pending

Differential operators on locally analytic Shimura varieties

Yuanyang Jiang

The locally analytic infinite-level Shimura variety can be fully reconstructed purely from its perfectoid counterpart and its B_dR^+-thickening via Grothendieck-Messing theory and a reformulated Riemann-Hilbert correspondence.

arxiv:2604.09116 v2 · 2026-04-10 · math.NT · math.AG

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\pithnumber{E4I6IXPHEP6J4VH4IEEKU4U3M6}

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4 Citations open

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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

The locally analytic infinite-level Shimura variety can be fully reconstructed purely from its perfectoid counterpart and its B_dR^+-thickening, via the Grothendieck-Messing theory combined with a reformulation of the Riemann-Hilbert correspondence.

C2weakest assumption

That the analytic stacks framework of Clausen-Scholze together with the reformulated Riemann-Hilbert correspondence actually produces a faithful reconstruction of the locally analytic Shimura variety from the perfectoid data and thickening.

C3one line summary

Constructs differential operators and a BGG-Fontaine complex on locally analytic Shimura varieties, conjecturing automorphic properties after establishing a reconstruction theorem from perfectoid data.

Cited by

1 paper in Pith

Classicality for Hilbert modular forms

Receipt and verification

First computed	2026-06-02T03:04:41.018009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2711e45de723fc9e54fc4108aa729b67bb707730604f1db82dcfd31f2b82f0dd

Aliases

arxiv: 2604.09116 · arxiv_version: 2604.09116v2 · doi: 10.48550/arxiv.2604.09116 · pith_short_12: E4I6IXPHEP6J · pith_short_16: E4I6IXPHEP6J4VH4 · pith_short_8: E4I6IXPH

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/E4I6IXPHEP6J4VH4IEEKU4U3M6 \
  | 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: 2711e45de723fc9e54fc4108aa729b67bb707730604f1db82dcfd31f2b82f0dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b929766f6b6927f25a8a10dc36dd3093c8ff73e1300605d756e43d53a019ea00",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-04-10T08:54:00Z",
    "title_canon_sha256": "5cfc06654b505ab73afe6a549ba73cc2368c06a9f73f62aec51432363c73a865"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.09116",
    "kind": "arxiv",
    "version": 2
  }
}