93 citations · 159 across the 27 of their papers we have counts for
27 papers
Arithmetic purity of strong approximation for toric varieties with constant global sections
Dasheng Wei, Fei Xu, Yi Zhu
Let be a smooth toric variety over a number field such that the global sections of are constant. We show that is dense in for…
Single conjugacy classes of isometries in orthogonal groups over local fields
Fei Xu, Bo Zhang
All isometries in a quadratic space over a non-archimedean local field of characteristic not 2 satisfying that any isometry which is conjugate to in the general linear…
Modulated categories and their representations via higher categories
Fei Xu, Maoyin Zhang
We consider the 3-category whose objects are 2-categories, 1-morphisms are lax functors, 2-morphisms are lax transformations and 3-morphisms are modifications. Th…
Integral embeddings of central simple algebras over number fields
Jiaqi Xie, Fei Xu
A criterion for determining exactly when an order of a maximal subfield of a central simple algebra over a number field can be embedded into an order of this algebra is given. Vari…
On cohomological characterizations of endotrivial modules
Fei Xu, Chenyou Zheng
Given a general finite group , there are various finite categories whose cohomology theories are of great interests. Recently Balmer and Grodal gave some new characterizations o…
Skew category algebras and modules on ringed finite sites
Mawei Wu, Fei Xu
Let be a small category. We investigate ringed sites on and the resulting module categories $\mathfrak{M}{\rm od}\text{-}\ma…
On indefinite -universal integral quadratic forms over number fields
Zilong He, Yong Hu, Fei Xu
An integral quadratic lattice is called indefinite -universal if it represents all integral quadratic lattices of rank for a given positive integer . For , we pr…
Counting integral points on indefinite ternary quadratic equations over number fields
Fei Xu, Runlin Zhang
We study an asymptotic formula for counting integral points over an equation defined by a non-degenerated indefinite integral ternary quadratic form representing a non-zero int…
On sheaves in finite group representations
Tengfei Xiong, Fei Xu
Given a general finite group , we consider several categories built on it, their Grothendieck topologies and resulting sheaf categories. For a certain class of transporter categ…
On indefinite and potentially universal quadratic forms over number fields
Fei Xu, Yang Zhang
A number field admits a binary integral quadratic form which represents all integers locally but not globally if and only if the class number of is bigger than one. In this…
Brauer-Manin obstruction for Markoff surfaces
J. -L. Colliot-Thélène, Dasheng Wei, Fei Xu
Ghosh and Sarnak have studied integral points on surfaces defined by an equation x^2+y^2+z^2-xyz= m over the integers. For these affine surfaces, we systematically study the Brauer…
Strong approximation for a family of norm varieties
Yang Cao, Dasheng Wei, Fei Xu
We study strong approximation of the equation N_{L/k}(x) = \prod_{i=1}^n p_i(t) where L/k is a finite extension of number fields and p_i(t)'s are distinct irreducible polynomials o…
Local Representation Theory of Transporter Categories
Fei Xu
We attempt to generalize the -modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our ta…
On homology with coefficients and generalized inductions
Fei Xu
In group representations several inductions given by tensoring with appropriate bimodules may be reconstructed via homology of -posets with -equivariant coefficients. For thi…
Arithmetic purity of strong approximation for homogeneous spaces
Yang Cao, Yongqi Liang, Fei Xu
We prove that any open subset of a semi-simple simply connected quasi-split linear algebraic group with over a number field satisfies stro…
Comparing descent obstruction and Brauer-Manin obstruction for open varieties
Yang Cao, Cyril Demarche, Fei Xu
We provide a relation between Brauer-Manin obstruction and descent obstruction for torsors over open varieties under a connected linear algebraic group or a group of multiplicative…
Strong approximation with Brauer-Manin obstruction for groupic varieties
Yang Cao, Fei Xu
Strong approximation with Brauer-Manin obstruction is established for smooth varieties containing a connected linear algebraic group with a compatible action.
Strong approximation for certain quadric fibrations with compact fibers
Fei Xu
In this paper, we will show that strong approximation with Brauer-Manin obstruction holds for certain quadratic fibration such that none of fibers satisfies strong approximation wi…
Very strong approximation for certain algebraic varieties
Qing Liu, Fei Xu
Let F be a global field. In this work, we show that the Brauer-Manin condition on adelic points for subvarieties of a torus T over F cuts out exactly the rational points, if either…
Strong approximation with Brauer-Manin obstruction for toric varieties
Yang Cao, Fei Xu
For smooth open toric varieties, we establish strong approximation off infinity with Brauer-Manin obstruction.
Spectra of tensor triangulated categories over category algebras
Fei Xu
Let C be a finite EI category and k be a field. We consider the category algebra kC. Suppose K(C)=D^b(kC-mod) is the bounded derived category of finitely generated left modules. Th…
Counting Integral Points in Certain Homogeneous Spaces
Dasheng Wei, Fei Xu
The asymptotic formula of the number of integral points in non-compact symmetric homogeneous spaces of semi-simple simply connected algebraic groups is given by the average of the…
Strong approximation for the total space of certain quadric fibrations
Jean-Louis Colliot-Thélène, Fei Xu
We study equations in four variables (x,y,z,t) of the shape q(x,y,z)=P(t), where q(x,y,z) is an indefinite ternary quadratic form over the integers and P(t) is a polynomial in one…
Support varieties for transporter category algebras
Fei Xu
Let G be a finite group. Over any finite G-poset P we may define a transporter category as the corresponding Grothendieck construction. The classifying space of the transporter cat…