We investigate the relations between the Poissonnian loop ensembles, their occupation fields, non ramified Galois coverings of a graph, the associated gauge fields, and random Eulerian networks.

Unramified coverings of the affine line in characteristic two are constructed having alternating groups as Galois groups. The proof uses Jacobson’s criterion for the Galois group of an equation to be contained in the alternating group. Alternative proofs use the Berlekamp discriminant or the Revoy discriminant. These are related to the Arf invariant.

We examine basic notions of categorical Galois theory for the adjunction between Π0 and the inclusion as discrete, in the case of simplicial complexes. Covering morphisms are characterized as the morphisms satisfying the unique simplex lifting property, and are classified by means of the fundamental groupoid, for which we give an explicit “Galoistheoretic” description. The class of covering mor...

We classify and study trigonal curves in Hirzebruch surfaces admitting dihedral Galois coverings. As a consequence, we obtain certain restrictions on the fundamental group of a plane curve D with a singular point of multiplicity (deg D−3).

We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we prove that there exists a universal Galois covering whose group of automorphisms is free and depends only on the derived category of the algebra. As a corollary...