Cocompleteness over coverings

Coverings of singular curves over finite fields

Enumerating branched coverings over surfaces with boundaries

The number of nonisomorphic n-fold branched coverings over a given surface with a boundary is determined by the number of nonisomorphic n-fold graph coverings over a suitable bouquet of circles. A similar enumeration can be done for regular branched coverings. Some explicit formulae for enumerations are also obtained. © 2003 Elsevier Ltd. All rights reserved. MSC 2000: 05C10; 05C30; 57M12

Quantale-valued preorders: Globalization and cocompleteness

Each divisible and unital quantale is associated with two quantaloids. Categories enriched over these two quantaloids can be regarded respectively as crisp sets endowed with fuzzy preorders and fuzzy sets endowed with fuzzy preorders. This paper deals with the relationship between these two kinds of enriched categories. This is a special case of the change-base issue in enriched category theory...

Abelian Étale Coverings of Modular Curves over Local Fields

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).

Enumerating branched orientable surface coverings over a non-orientable surface

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...