Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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24 May 2016
TL;DR: In this article, the authors studied duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes over a local ring for a finite field.
Abstract: In this thesis, we study duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes $X$ over a local ring $\mathbb{F}_q[[t]]$, for a finite field $\mathbb{F}_q$. As an application, we obtain a new filtration on the maximal abelian quotient $\pi^{\text{ab}}_1(U)$ of the \'etale fundamental groups $\pi_1(U)$ of an open subscheme $U \subseteq X$, which gives a measure of ramification along a divisor $D$ with normal crossing and $\text{Supp}(D) \subseteq X-U$. This filtration coincides with the Brylinski-Kato-Matsuda filtration in the relative dimension zero case.
2 citations
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01 Jun 2016
TL;DR: In this paper, the authors give an asymptotic formula for the mean square of �(a;x) under a certain condition, where k = 2 and k = 3.
Abstract: Let a = (a1,a2,...,ak), where aj (j = 1,...,k) are positive integers such that a1 ≤ a2 ≤ ··· ≤ ak. Let d(a;n) = P n a1 1 ···n ak k =n 1 and �(a;x) be the error term of the summatory function of d(a;n). In this paper we show an asymptotic formula of the mean square of �(a;x) under a certain condition. Furthermore, in the cases k = 2 and 3, we give unconditional asymptotic formulas for these mean squares.
2 citations
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TL;DR: In this paper, the greatest solutions of systems of linear equations over a lattice (P, ≤) were derived for a pseudocomplemented lattice, where a matrix A has a right inverse over a distributive lattice if and only if A is a column orthogonal over the lattice.
Abstract: We compute the greatest solutions of systems of linear equations over a lattice (P, ≤). We also present some applications of the results obtained to lattice matrix theory. Let (P, ≤) be a pseudocomplemented lattice with
$$\widetilde0$$
and
$$\widetilde1$$
and let A = ‖a
ij
‖
n×n
, where a
ij
∈ P for i, j = 1,..., n. Let A* = ‖a
′
‖
n×n
and
$$
a_{ij} ' = \mathop \Lambda \limits_{r = 1r
e j}^n a_{ri}^*
$$
for i, j = 1,..., n, where a* is the pseudocomplement of a ∈ P in (P, ≤). A matrix A has a right inverse over (P, ≤) if and only if A · A* = E over (P, ≤). If A has a right inverse over (P, ≤), then A* is the greatest right inverse of A over (P, ≤). The matrix A has a right inverse over (P, ≤) if and only if A is a column orthogonal over (P, ≤). The matrix D = A · A* is the greatest diagonal such that A is a left divisor of D over (P, ≤). Invertible matrices over a distributive lattice (P, ≤) form the general linear group GL
n
(P, ≤) under multiplication. Let (P, ≤) be a finite distributive lattice and let k be the number of components of the covering graph Γ(join(P,≤) −
$$\{ \widetilde0\} $$
, ≤), where join(P, ≤) is the set of join irreducible elements of (P, ≤). Then GL
a
(P, ≤) ≅ = S
. We give some further results concerning inversion of matrices over a pseudocomplemented lattice.
2 citations
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TL;DR: In this article, it was shown that the anti-pluricanonical map is birational when $m\geq 16$ for $5$-fold $X$ whose anticanonically divisor is large and big.
Abstract: We prove that the anti-pluricanonical map $\Phi_{|-mK_{X}|}$ is birational when $m\geq 16$ for $5$-fold $X$ whose anticanonical divisor is nef and big.
2 citations
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TL;DR: In this article, the authors classify finite solvable groups whose character tables have at most p + 1 zeros in each column, where p is the minimal prime divisor of their orders.
Abstract: In the present paper, the authors classify finite solvable groups whose character tables have at most p + 1 zeros in each column, where p is the minimal prime divisor of their orders. MSC: 20C15
2 citations