相关论文: General base change for relative Du Bois complexes

We give a $\delta$-constant criterion for equinormalizability of deformations of isolated (not necessarily reduced) curve singularities over smooth base spaces of dimension $\geq 1$. For one-parametric families of isolated curve…

Let $G$ be a generically reductive group over a smooth projective curve $X$ over a finite field. For any finite set $I$, we show that nearby cycles commute with proper direct image from stacks of shtukas to $X^I$. This generalizes some…

We continue our study of the well-posedness theory of a one-parameter family of coupled KdV-type systems in the periodic setting. When the value of a coupling parameter \alpha \in (0, 4) \setminus 1, we show that the Gibbs measure is…

A general proposition is proved relating multiplicities (of restriction of a representation of a group to a subgroup) under basechange, and used to calculate some multiplicities for cuspidal representations which become principal series…

This paper studies the behavior of Grobner bases with respect to extensions of scalars. We prove that an extension of scalars commutes with taking Grobner bases iff the extension is flat. We consider what information can be deduced about…

We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…

We extend our previous result on the behavior of the quadratic part of a complex points of a small $\mathcal{C}^{2}$-perturbation of a real $4$-manifold embedded in a complex $3$-manifold. We describe the change of the structure of a normal…

We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically…

We show that a generically sharply $t$-transitive permutation group of finite Morley rank on a set of rank $r$ satisfies $t\le r+2$ provided the pointwise stabilizer of a generic $(t-1)$-tuple is an $L$-group, which holds, for example, when…

We formulate a quantization commutes with reduction principle in the setting where the Lie group $G$, the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and…

This work establishes simple criteria for detecting higher rational singularities via the intersection Du Bois complex and the irrationality complex of a normal variety over the complex numbers.

This result generalizes a previous result established in [2] where the Absolute Constants of the Koras-Russell threefold was shown to be invariant under translates in the base field to the Absolute Constants of the Koras-Russell threefold…

For a group $G$ and a subset $X$ of $G$, the commuting graph of $X$, denoted by $\Gamma(G,X)$ is the graph whose vertex set is $X$ and any two vertices $u$ and $v$ in $X$ are adjacent if and only if they commute in $G$. In this article,…

Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…

We define the notion of universal lift of a projective complex based on non-commutative parameter algebras, and prove its existence and uniqueness. We investigate the properties of parameter algebras for universal lifts.

We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…

We consider a broad matrix parameterized family of pseudo-differential calculi, containing the usual Shubin's family of pseudo-differential calculi, parameterized by real numbers. We show that continuity properties in the framework of…

Using the moduli space of semiorthogonal decompositions in a smooth projective family, introduced by the second, the third and the fourth author, we propose a novel approach to indecomposability questions for derived categories. Modulo a…

We consider some algebraic aspects of the dynamics of an automorphism on a family of polarized abelian varieties parameterized by the complex unit disk. When the action on the cohomology of the generic fiber has no cyclotomic factor, we…

Several algebraic criteria, reflecting displacement properties of transformation groups, have been used in the past years to prove vanishing of bounded cohomology and stable commutator length. Recently, the authors introduced the property…