Related papers: Module sectional category of products
We study weak approximation on rationally connected varieties under an assumption of strong approximation for a "simple" variety or under Schinzel's hypothesis. We also get some unconditional results.
Schwarz genus $\mathsf{g}(\xi)$ of a fibration $\xi\colon E\to B$ is defined as the minimal integer $n$, such that there exists a cover of $B$ by $n$ open sets that admit partial section to $\xi$. Many important concepts, including…
Fractional variation is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. Fractional velocity can be suitable for characterizing singular behavior of derivatives…
We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a…
For a regular normal element in an arbitrary ring, we study the category of its module factorizations. The cokernel functor relates module factorizations with Gorenstein projective components to Gorenstein projective modules over the…
We construct an explicit semifree model for the fiber join of two fibrations p: E --> B and p': E' --> B from semifree models of p and p'. Using this model, we introduce a lower bound of the sectional category of a fibration p which can be…
The categorical formulation of the Eilenberg-Watts calculus relates, for any pair of finite categories M and N, the finite categories Fun^{le}(N,M) and Fun^{re}(N,M) of linear left or right exact functors and the Deligne product \bar N…
We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…
About last 70s, Haynsworth [6] used a result of the Schur complement to refine a determinant inequality for positive definite matrices. Haynsworth's result was improved by Hartfiel [5]. We extend their result to a larger class of matrices,…
Let $\mathcal{X}$ be a semibrick in an extriangulated category $\mathscr{C}$. Let $\mathcal{T}$ be the filtration subcategory generated by $\mathcal{X}$. We give a one-to-one correspondence between simple semibricks and length wide…
We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood…
We (re)consider how the Fukaya category of a Lefschetz fibration is related to that of the fibre. The distinguishing feature of the approach here is a more direct identification of the bimodule homomorphism involved.
We study the moduli functor of flat bundles on smooth, possibly non-proper, algebraic variety $X$ (over a field of characteristic zero). For this we introduce the notion of \emph{formal boundary} of $X$, denoted by $\partial X$, which is a…
Let $\mathrm{VI}$ be the category of finite dimensional $\mathbb{F}_q$-vector spaces whose morphisms are injective linear maps, and let $\mathbf{k}$ be a noetherian ring. We study the category of functors from $\mathrm{VI}$ to…
It is known that finite crossed modules provide premodular tensor categories. These categories are in fact modularizable. We construct the modularization and show that it is equivalent to the module category of a finite Drinfeld double.
We extend the definition of a semidualizing module to associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule C. We then study the classes of C-flats, C-projectives, and…
We show that the conditions in Steimle's 'additivity theorem for cobordism categories' can be weakened to only require \emph{locally} (co)Cartesian fibrations, making it applicable to a larger class of functors. As an application we compute…
In this paper some axiomatic generalization (function of open subsets) of the relative Lyusternik-Schnirelmann category is considered, incorporating the sectional category and the Schwarz genus as well. For this function and a given…
This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…
We calculate the Borel-Moore homology of affine Springer fibers of type $A$ associated to some regular semisimple nil elliptic elements. As a result, we obtain bigraded $\mf{S}_{n}$-modules whose bigraded Frobenius series are generalization…