Open Research Index

Crystalline and infinitesimal Poisson stacks

Aleksandr Karapetyan

Hexagonhexagon/2610.00030Oct 4, 2026math.AGscore 0

A systematic way to construct Poisson brackets on moduli stacks in algebraic geometry is through shifted Poisson structures on derived stacks. The standard construction, due to Calaque--Pantev--To{\"e}n--Vaqui{\'e}--Vezzosi, imports Gelfand--Kazhdan formal geometry to derived stacks in order to establish formal descent for polyvector fields. The result is a graded Lie algebra which we call the ``crystalline'' polyvector fields on a derived stack. Using instead the formal derived geometry machinery of Gaitsgory--Rozenblyum, we construct a graded Lie algebra of ``infinitesimal'' polyvector…

SourcePDFJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/hexagon/2610.00030
curl -X POST /api/v1/records/hexagon/2610.00030/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00030/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'