相关论文: On a Conjecture of Colliot-Thelene
We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…
The purpose of these notes is describe the state of progress on the restriction problem in harmonic analysis, with an emphasis on the developments of the past decade or so on the Euclidean space version of these problems for spheres and…
We show the Farrell-Jones conjecture with coefficients in left-exact $\infty$-categories for finitely $\mathcal{F}$-amenable groups and, more generally, Dress-Farrell-Hsiang-Jones groups. Our result subsumes and unifies arguments for the…
Let K be an algebraically closed field of prime characteristic p, let X be a semiabelian variety defined over a finite subfield of K, let f be a regular self-map on X defined over K, let V be a subvariety of X defined over K, and let x be a…
We reinterpret a conjecture of Breuil on the locally analytic $\mathrm{Ext}^1$ in a functorial way using $(\varphi,\Gamma)$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or…
It is shown that if the generalized Hodge conjecture, or some weaker form of it, holds for a Calabi-Yau variety then it holds for any Calabi-Yau variety birationally equivalent to it. The key idea is to construct suitable homomorphisms…
The goal of this paper is to establish Beilinson-Bernstein type localization theorems for quantizations of some conical symplectic resolutions. We prove the full localization theorems for finite and affine type A Nakajima quiver varieties.…
By computing all cyclotomic points on some algebraic varieties, we get an independent and efficient way to find all rational $a^3b$-monotiles for the sphere, thereby completing the classification of edge-to-edge monohedral quadrilateral…
An abstract, Hales-Jewett type extension of the polynomial van der Waerden Theorem [J. Amer. Math. Soc. 9 (1996),725-753] is established: Theorem. Let r,d,q \in \N. There exists N \in \N such that for any r-coloring of the set of subsets of…
A recent paper [R22] established "Frobenius reciprocity" as a bijection $t$ between certain symplectically reduced spaces (which need not be manifolds), and conjectured: 1{\deg}) $t$ is a diffeomorphism when these spaces are endowed with…
We introduce the notion of a point on a locally closed subset of a symplectic manifold being "locally rigid" with respect to that subset, prove that this notion is invariant under symplectic homeomorphisms, and show that coisotropic…
It is known that isomorphisms of graph Jacobians induce cyclic bijections on the associated graphs. We characterize when such cyclic bijections can be strengthened to graph isomorphisms, in terms of an easily computed divisor. The result…
We study Deligne's conjecture on the monodromy weight filtration on the nearby cycles in the mixed characteristic case, and reduce it to the nondegeneracy of certain pairings in the semistable case. We also prove a related conjecture of…
Generalizing de Vries Compactification Theorem and strengthening Leader Local Compactification Theorem, we describe the partially ordered set $(\LL(X),\le)$ of all (up to equivalence) locally compact Hausdorff extensions of a Tychonoff…
Following Schmidt, Thurnheer and Bugeaud-Kristensen, we study how Dirichlet's theorem on linear forms needs to be modified when one requires that the vectors of coefficients of the linear forms make a bounded acute angle with respect to a…
Closely following recent ideas of J. Borcea, we discuss various modifications and relaxations of Sendov's conjecture about the location of critical points of a polynomial with complex coefficients. The resulting open problems are formulated…
Properties of local and global slope of a function and its approximate critical points sets are studied in relation to determination of the function.
We introduce the notion of a Bredon-style equivariant coarse homology theory. We show that such a Bredon-style equivariant coarse homology theory satisfies localization theorems and that a general equivariant coarse homology theory can be…
In this note we give generalizations and prove 'minimalistic' refinements of the t-birational Section Conjecture (t-BSC), cf. [Be], by doing both: First, by extending the class of base fields over which the t-BSC holds, and second, by…
Malec and Tompkins (EUJC, 2023) considered the localized versions of Tur\'an-type problems, and proved a localized theorem on Erd\H{o}s-Gallai Theorem on paths. Zhao and Zhang (JGT, 2025) gave a long proof of a localized version of…