We define generalizations of classical invariants of ramification, for coverings on a variety of arbitrary dimension over a local field of mixed characteristic. For an -adic sheaf, we define its Swan class as a 0-cycle class supported on the closed fiber. We present a formula for the Swan conductor of cohomology and its relative version. Let K be a complete discrete valuation field of character...

A covering of a multigraph G is a subset of edges which meet ail vertices of G. Partitions of the edges of G into coverings Ci, C2,..., Ck are considered. In particular we examine how close the cardinalities of thèse coverings may be. A resuit concerning matchings is extended to the décomposition into coverings. Finally thèse considérations are generalized to the décompositions of the vertices ...

Abstract. A general greedy approach to construct coverings of compact metric spaces by metric balls is given and analyzed. The analysis is a continuous version of Chvátal’s analysis of the greedy algorithm for the weighted set cover problem. The approach is demonstrated in an exemplary manner to construct efficient coverings of the n-dimensional sphere and n-dimensional Euclidean space to give ...

A proof of a conjecture for the number of ramified coverings of the sphere by the torus * Abstract An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson and Vainshtein for the explicit number of such co...

In this work we deal with coverings and actions of Lie groupgroupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids. Later, we show the equivalence of the category of smooth actions of Lie group-groupoids on Lie groups and the category of smooth coverings of Lie group-groupoids.

BACKGROUND Maximal sterile barrier precautions (MSBP) including head coverings and face masks are advocated for use in invasive procedures, including coronary interventions. The rationale for MSBP assumes it is an obligatory measure for infection prevention. However, in many coronary catheterization laboratories, head coverings/face masks are not used in daily practice. This study prospectively...

We report on two classes of autoequivalences of the category of Yetter-Drinfeld modules over a finite group, or, equivalently the Drinfeld center of the category of representations of a finite group. Both operations are related to the r-th power operation, with r relatively prime to the exponent of the group. One is defined more generally for the group-theoretical fusion category defined by a f...

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...

Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP-Galois extensions), (2) faithfully Galois extensions, and (3) H-separable Galois extensions. Moreover, it is shown that the intersection of the class of CP-Galois extensions and the class of faithfully Galois extensions is the class of Azumaya Galois extensions.

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph Gq(n, r) by subspaces from the Grassmann graph Gq(n, k), k ≥ r , are discussed. The problem is of interest from four points of view: coding theory, combinatorial designs, q-analogs, and projective geometry. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and...