  We identify the fractions of supersymmetry preserved by the most general
warped flux AdS and flat backgrounds in both massive and standard IIA
supergravities. We find that $AdS_n\times_w M^{10-n}$ preserve $2^{[{n\over2}]}
k$ for $n\leq 4$ and $2^{[{n\over2}]+1} k$ for $4<n\leq 7$ supersymmetries,
$k\in \bN_{>0}$. In addition we show that, for suitably restricted fields and
$M^{10-n}$, the killing spinors of AdS backgrounds are given in terms of the
zero modes of Dirac like operators on $M^{10-n}$. This generalizes the
Lichnerowicz theorem for connections whose holonomy is included in a general
linear group. We also adapt our results to $\bR^{1,n-1}\times_w M^{10-n}$
backgrounds which underpin flux compactifications to $\bR^{1,n-1}$ and show
that these preserve $2^{[{n\over2}]} k$ for $2<n\leq 4$, $2^{[{n+1\over2}]} k$
for $4<n\leq 8$, and $2^{[{n\over2}]} k$ for $n=9, 10$ supersymmetries.
