We develop a representation theoretic technique for detecting closed orbits that is applicable in all characteristics. Our based on Kempf’s theory of optimal subgroups and we make some improvements simplify the from computational perspective. exhibit our many examples particular, give an algorithm to decide if symmetric polynomial $n$-variables has $\operatorname{SL}\_n$-orbit. As important app...

with respect to étale cohomology with compact supports. This relation fails in general for l = p, but holds in an important special case. Suppose f is a Galois cover and deg f is a power of p. Then the relation χc(X,Qp) = (deg f)χ(Y,Ql) holds; for complete curves, this is due to Shafarevich [2], for arbitrary curves it is equivalent to the Deuring-Shafarevich formula, and in general it is due t...