We relate a part of the abelian étale fundamental group of curves over local fields to the component group of the Néron model of the jacobian. We apply the result to the modular curve X0(p)/Qp to show that the unramified abelian covering X1(p) → X0(p) (Shimura covering) uses up all the possible ramification over the special fiber of X0(p).

Article history: Received 15 April 2014 Received in revised form 29 September 2014 Accepted 28 October 2014 Available online 4 November 2014

Let F denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class F which are n-fold symmetric, where n is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. T f2F f ðDÞ and S f2F f ðDÞ. Moreover, the Koebe constant and the covering consta...

For every fixed graph H, we determine the H-covering number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, C(H,Kn) = d dn 2h dn− 1 d ee, unless d is even, n = 1 mod d and n(n− 1)/d+ 1 = 0 mod (2h/d), in which case C(H,Kn) = d ( n 2 ) h e+ 1. Our m...

In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, has a standard connecting component), then it has Galois coverings associated to the coverings of the connecting component. As a consequence, the first Hochschild cohomology group of a standard laura algebra vanishes if and only if it has no proper Galois coverings.

We calculate the metric on the D-brane vacuum moduli space for backgrounds of the form C 3 /Γ for cyclic groups Γ. In the simplest procedure — starting with a flat " seed " metric on the covering space — we find that the resulting D-brane metric is not Ricci-flat. We argue that this is likely to be true of the true 0-brane metric at weak string coupling.

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c, c′) and Hom(c′, c) is nonempty for c 6= c′. If we keep in place the latter axiom but allow for more than one morphism between objects, we have a sort of generalized poset in which there are multiplicities attached to the covering relations, and possibly nontrivial au...