symmetric monoidal (∞,1)-category of spectra
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
$\infty$-Lie groupoids
$\infty$-Lie groups
$\infty$-Lie algebroids
$\infty$-Lie algebras
This entry provides some links concerning the notes
This text establishes a statement (theorem 5.3) that characterizes ∞-stacks over an (∞,1)-site of formal duals of Artin E-∞ algebras over a field (hence infinitesimally thickened points in derived geometry) such that
they have a contractible underlying ∞-groupoid
(in the terminology and notation for cohesive (∞,1)-toposes)
and are infinitesimally cohesive in that they respects homotopy fiber products of morphisms whose kernels are nilpotent ideals
with those associated to an ∞-Lie algebra $\mathfrak{g}$ in the sense of (Hinich). This is (Lurie, theorem 0.0.13, remark 0.0.15).
The construction is then generalized to noncommutative geometry.
Am earlier (2007) model category-presentation proof by (Pridham) exists, see the discussion at
A indication of how to use the main theorem here in order to implement Lie differentiation of smooth ∞-groups is at
The same result was proved earlier (theorem 2.30 and corollary 4.57, cf (Lurie, remark 0.0.14)), with further model category presentations and comparisons, in
See at model structure for L-infinity algebras for more along these lines.
The foundations of the theory appear in
For more related discussion see also
A survey is in
Last revised on November 5, 2022 at 09:10:05. See the history of this page for a list of all contributions to it.