derived smooth geometry
The space of infinitesimal loops in a given space.
With a suitable scheme, its formal loop space in the sense of (Kapranov-Vasserot I) has a Tate structure? and hence an associated determinantal gerbe with band? . According to (Kapranov-Vasserot IV) this gerbe is essentially identified with the gerbe of chiral differential operators on .
In the context of algebraic geometry formal loop spaces have been introduced and studied in
Tentative aspects of a generalization to differential geometry are discussed in