Richard Garbary, Pure Mathematics, University of Waterloo
“More about completeness”
Last
time
we
discussed
our
algebraic
analogue
of
compactness.
More
precisely,
a
variety
V
over
a
field
k
is
said
to
be
complete
(over
k)
if
for
all
varieties
W
over
k,
the
map
V
×W
→
W
is
closed.
I’m
going
to
talk
about
some
properties
of
completeness.
This
will
include
why
a
map
from
a
complete
variety
to
an
affine
variety
must
collapse
everything
to
a
point,
and
why
completeness
is
stable
under
base
change.