We introduce the notion of ascent sliceness of virtual knots. A representative of a virtual knot is an embedding S1↪Σg×I, for Σg
Nearby in the stack
a closed connected oriented surface of genus
g
; the virtual knot represented is slice if there exists a pair consisting of a disc
D
and an oriented
3
-manifold
M
, such that
D↪M×I
,
∂M=Σg
, and
∂D=S1
(the image of the embedding). This definition of sliceness exemplifies that a cobordism of virtual links is a pair consisting of a surface and a
3
-manifold; in addition to analysing the surfaces, as is done in classical knot theory, we may analyse the
3
-manifolds appearing in cobordisms between virtual knots. In particular, consider a Morse function on the
3
-manifold
M
: away from critical points the level sets are surfaces, and we may ask how the genus of these surfaces changes as we move through the cobordism. Roughly, a slice virtual knot
K
with genus-minimal representative
S1↪Σg×I
is ascent slice if, given any disc and
3
-manifold pair
(D,M)
as above, and any Morse function
f:M→I
, the surface
Σg+1
appears as a level set of
f
. We use an augmented version of doubled Khovanov homology to define a property which implies ascent sliceness for slice virtual knots of minimal supporting genus