  We interpret syntomic cohomology of Nekov\'a\v{r}-Nizio{\l} as a $p$-adic
absolute Hodge cohomology. This is analogous to the interpretation of
Deligne-Beilinson cohomology as an absolute Hodge cohomology by Beilinson and
generalizes the results of Bannai and Chiarellotto, Ciccioni, Mazzari in the
good reduction case, and of Yamada in the semistable reduction case. This
interpretation yields a simple construction of the syntomic descent spectral
sequence and its degeneration for proper and smooth varieties. We introduce
syntomic coefficients and show that in dimension zero they form a full
triangulated subcategory of the derived category of potentially semistable
Galois representations.
  Along the way, we obtain $p$-adic realizations of mixed motives including
$p$-adic comparison isomorphisms. We apply this to the motivic fundamental
group generalizing results of Olsson and Vologodsky.
