For a scheme, analogous to how an -scheme is a scheme over , a -scheme is a scheme over the de Rham space of .
See also diffiety.
For a scheme, a -scheme is a scheme over the de Rham space of .
Relation to D-modules
This is (BeilinsonDrinfeld, section 2.3).
This is indeed equivalent to the above abstract definition
This appears as (Lurie, theorem, 0.6 and below remark 0.7)
Relation to jet schemes
The free -scheme on a given -scheme is the jet bundle of .
This is (BeilinsonDrinfeld, 2.3.2).
This fact makes -geometry a natural home for variational calculus.
The definition in terms of monoids in D-modules is in section 2.3 in
The observation that this is equivalent to the abstract definition given above appears in pages 5 and 6 of
- Jacob Lurie, Notes on crystals and algebraic -modules
Revised on June 22, 2011 16:18:00
by Urs Schreiber