Superdomain
See
lectures of J. Bernstein1 Definition of superdomain
A superdomain 
of dimension 
is a pair 
where 
is an open set and
a supercommutative algebra.
We will call
the
body of
. We will also abbreviate:
For any
and
we define:
2 Morphisms of superdomains
A
morphism of superdomains
is a pair
where
is
a smooth map from the body of
to the body of
such that:
3 Sub-superdomain
Let 
be a superdomain and 
an open
subset of .
For any open subset
we consider a sub-superdomain
. Any
has a restriction
to
: just restrict
,
,
, ... to
. We will call the restriction
:
Let
be a morphism of superdomains.
Suppose that
is an open subset of
. Every morphism
can be restricted to
:
