let $f$ be a finite extension of $bbb q$‎, ‎${bbb q}_p$ or a global‎ ‎field of positive characteristic‎, ‎and let $e/f$ be a galois extension‎. ‎we study the realization fields of‎ ‎finite subgroups $g$ of $gl_n(e)$ stable under the natural‎ ‎operation of the galois group of $e/f$‎. ‎though for sufficiently large $n$ and a fixed‎ algebraic number field $f$ every its finite extension $e$ is‎ ‎re...

The regular coverings of regular affine algebraic maps are considered, and a large family of totally ramified coverings—the so-called Steinberg and Accola coverings—are fully classified.

The notion of a (pointed) Galois pretopos (“catégorie galoisienne”) was considered originally by Grothendieck in [12] in connection with the fundamental group of an scheme. In that paper Galois theory is conceived as the axiomatic characterization of the classifying pretopos of a profinite group G. The fundamental theorem takes the form of a representation theorem for Galois pretopos (see [10] ...

For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism ρ X : C X → π ab 1 (X), which is surjective and whose kernel is the connected component of the identity. The (topological) group C X is explicitly given and built solely out of data attached to points and curves on X. A similar but weaker statement holds for smooth varieties over fini...

Preface Why we called the class of two-dimensional Shimura varieties, which are not Hilbert modular, "Picard modular surfaces" ? In the mean time the name has been generally accepted, see e.g. Langlands (and others) L-R]. On the one hand Picard worked on special Fuchsian systems of diierential equations; on the other hand Shimura Shi] introduced and investigated moduli spaces of abelian varieti...

The main purpose is to characterise continuous maps that are n-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius n-homomorphisms between two function spaces that correspond to n-branched coverings are determined completely. Several equivalent definitions of a Frobenius n-homomorphism are compared and some of their properties are proved. A...

An almost Belyi covering is an algebraic covering of the projective line, such that all ramified points except one simple ramified point lie above a set of 3 points of the projective line. In general, there are 1-dimensional families of these coverings with a fixed ramification pattern. (That is, Hurwitz spaces for these coverings are curves.) In this paper, three almost Belyi coverings of degr...

We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.

The isomorphism classes of several types of graph coverings of a graph have been enumerated by many authors [M. Hofmeister, Graph covering projections arising from finite vector space over finite fields, Discrete Math. 143 (1995) 87–97; S. Hong, J.H. Kwak, J. Lee, Regular graph coverings whose covering transformation groups have the isomorphism extention property, Discrete Math. 148 (1996) 85–1...