The author presents a detailed analysis of 2-complete stable
homotopy groups, both in the classical context and in the motivic
context over $\mathbb C$. He uses the motivic May spectral sequence
to compute the cohomology of the motivic Steenrod algebra over
$\mathbb C$ through the 70-stem. He then uses the motivic Adams
spectral sequence to obtain motivic stable homotopy groups through
the 59-stem. He also describes the complete calculation to the
65-stem, but defers the proofs in this range to forthcoming
publications. In addition to finding all Adams differentials, the
author also resolves all hidden extensions by $2$, $\eta $, and
$\nu $ through the 59-stem, except for a few carefully enumerated
exceptions that remain unknown. The analogous classical stable
homotopy groups are easy consequences. The author also computes the
motivic stable homotopy groups of the cofiber of the motivic
element $\tau $. This computation is essential for resolving hidden
extensions in the Adams spectral sequence. He shows that the
homotopy groups of the cofiber of $\tau $ are the same as the
$E_2$-page of the classical Adams-Novikov spectral sequence. This
allows him to compute the classical Adams-Novikov spectral
sequence, including differentials and hidden extensions, in a
larger range than was previously known.
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