Search results for "Number"

Characters with stable irreducible constituents

1995

On π-blocks of finite groups

1985

Functional equations of the dilogarithm in motivic cohomology

2009

We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall demonstrate with a few examples, to write down enough relations in Bloch's integral higher Chow group CH^2(F,3) for certain number fields F to detect torsion cycles. Using the regulator map to Deligne cohomology, one can check the non-triviality of the torsion cycles thus obtained. Using this combination of methods, we obtain explicit higher Chow cycles generating the integral motivic cohomology groups of some number fields.

The associated graded module of the test module filtration

2017

We show that each direct summand of the associated graded module of the test module filtration $\tau(M, f^\lambda)_{\lambda \geq 0}$ admits a natural Cartier structure. If $\lambda$ is an $F$-jumping number, then this Cartier structure is nilpotent on $\tau(M, f^{\lambda -\varepsilon})/\tau(M, f^\lambda)$ if and only if the denominator of $\lambda$ is divisible by $p$. We also show that these Cartier structures coincide with certain Cartier structures that are obtained by considering certain $\mathcal{D}$-modules associated to $M$ that were used to construct Bernstein-Sato polynomials. Moreover, we point out that the zeros of the Bernstein-Sato polynomial $b_{M,f}$ attached to an \emph{$F$-…

Special arrangements of lines: Codimension 2 ACM varieties in P 1 × P 1 × P 1

2019

In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.

Complexity of gauge bounded Cartier algebras

2019

We show that a gauge bounded Cartier algebra has finite complexity. We also give an example showing that the converse does not hold in general.Communicated by Graham J. Leuschke

Coupled coincidence points for compatible mappings satisfying mixed monotone property

2012

We establish coupled coincidence and coupled fixed point results for a pair of mappings satisfying a compatibility hypothesis in partially ordered metric spaces. An example is given to illustrate our obtained results.

On a question of C. Bonnafé on characters and multiplicity free constituents

2019

Abstract In 2006, C. Bonnafe posed a general question on characters of finite groups. A positive answer would have reduced drastically some proofs by G. Lusztig.

Partial Multiplication of Operators in Rigged Hilbert Spaces

2005

The problem of the multiplication of operators acting in rigged Hilbert spaces is considered. This is done, as usual, by constructing certain intermediate spaces through which the product can be factorized. In the special case where the starting space is the set of C∞-vectors of a self-adjoint operator A, a general procedure for constructing a special family of interspaces is given. Their definition closely reminds that of the Bessel potential spaces, to which they reduce when the starting space is the Schwartz space \(\mathcal{S}(\mathbb{R}^n ).\) Some applications are considered.

Picard-Fuchs operators for octic arrangements, I: the case of orphans

2019

We report on $25$ families of projective Calabi-Yau threefolds that do not have a point of maximal unipotent monodromy in their moduli space. The construction is based on an analysis of certain pencils of octic arrangements that were found by C. Meyer. There are seven cases where the Picard-Fuchs operator is of order two and $18$ cases where it is of order four. The birational nature of the Picard-Fuchs operator can be used effectively to distinguish between families whose members have the same Hodge numbers.