  In order to compute with $l$--adic sheaves or crystals on a line over
$\mathbb{F} _q$ a low-technology alternative to the traditional computation
with the Hecke operators on the automorphic side could be helpful. A program
which has evolved over the years in our discussions with M. Kontsevich centers
around the concept that, in the geometric case, there must exist certain
multiplication laws on the Galois--representation side that could be thought of
as precursors of the automorphic lifts: non-abelian Abel's theorems, and their
restrictions to diagonal, Clausen identities. To a varying extent, they can
determine the trace functions of $l$--adic sheaves or crystals with prescribed
ramification without directly appealing to the Hecke--eigen property on the
automorphic side.
