Ternary quartics and 3-dimensional commutative algebras.
Explicit formulae for the number of triplets of consecutive squares in a Galois field are given.
In this article, we prove that a -homology plane with two algebraically independent -actions is isomorphic to either the affine plane or a quotient of an affine hypersurface in the affine -space via a free -action, where is the order of a finite group .
We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.
We determine the algebraic groups which have a close relation to the Roth inequalities.