We compute the cohomology of the subalgebra
AC2(1) of the
C2-equivariant Steenrod
algebra
AC2. This serves as the
input to the
C2-equivariant
Adams spectral sequence converging to the completed
RO(C2)-graded
homotopy groups of an equivariant spectrum
koC2. Our approach is to
use simpler
C-motivic
and
R-motivic
calculations as stepping stones.
Keywords
Adams spectral sequence, motivic homotopy, equivariant
homotopy, equivariant K-theory, cohomology of the Steenrod
algebra