Lukas Brantner: Formal integration of derived foliations

Abstract.

Frobenius' theorem in differential geometry asserts that every involutive subbundle \(E \subset TM\) of the tangent bundle of a manifold \(M\) integrates to a decomposition of \(M\) into smooth leaves. We prove an infinitesimal analogue for suitably nice schemes \(X\) over coherent base rings, showing that every partition Lie algebroid \(\mathfrak{g} \to T_X\) integrates uniquely to a formal moduli stack \(X \to S\) under \(X\), where \(S\) is the formal leaf space and the fibres of \(X \to S\) are the formal leaves. This talk is based on joint work with Magidson-Nuiten, and ties into the work of Jiaqi Fu.