  This is a common introduction to math.RT/0101170, math.RT/0306333,
math.RT/0506043, math.RT/0601028. Compared to these references there are new
results including (i) a description of a separable closure of an extension of
transcendence degree one of an algebraically closed field of positive
characteristic; (ii) a "K\"unneth formula" for the products with curves; (iii)
the semi-simplicity of the module of regular forms of top degree
$\Omega^n_{F/k}$.
