Induction and restriction in formal deformation of coverings

Parabolic induction and the Harish-Chandra D-module

Let G be a reductive group and L a Levi subgroup. Parabolic induction and restriction are a pair of adjoint functors between Ad-equivariant derived categories of either constructible sheaves or (not necessarily holonomic) D-modules on G and L, respectively. Bezrukavnikov and Yom Din proved, generalizing a classic result of Lusztig, that these functors are exact. In this paper, we consider a special case where L=T is a maximal torus. We give explicit formulas for parabolic induction and restriction in terms of the Harish-Chandra D-module on G x T. We show that this module is flat over D(T), whi…

Hypersurface singularities in positive characteristic

The paper is motivated on the open problem of resolution of singularities in positive characteristic. The aim is to present a form of induction which is different from that used by Hironaka. In characteristic zero induction is formulated by restriction to smooth hypersurfaces (hypersurfaces of maximal contact). Our alternative approach, introduced here, replaces restrictions to smooth sub-schemes by generic projections on smooth schemes of smaller dimension. We also introduce a generalization of the discriminant, and our result makes use of the elimination theory. In the case of fields of char…

商栈的上同调 Mackey 公式

Cohomological Mackey formula for quotient stacks

该研究针对等变 Landau–Ginzburg 模型的临界上同调，构造限制态射并证明其与归纳映射满足 Mackey 型相容公式，使其具有局部化归纳–限制系统结构。

Verdier 特化与 Hodge 模块的限制

Verdier specialization and restrictions of Hodge modules

本文利用 Verdier 特化与 $V$-过滤给出光滑簇闭浸入下 Hodge 模块上同调拉回函子的显式公式，并通过对余维数归纳提供了该定理的简化证明。

Deformations of Lie algebras and Induction of Schemes

Let $Ł_m$ be the scheme of the laws defined by the identities of Jacobi on $\K^m$. The local studies of an algebraic Lie algebra $\g=\mathrm{R}\ltimes\n$ in $Ł_m$ and its nilpotent part $\n$ in the scheme $Ł_n^{\mathrm{R}}$ of $\mathrm{R}$-invariant Lie algebras on $\K^n$ are linked. This comparison is made by means of slices, which are transversal subschemes to the orbits of $\g$ and $\n$ under the classical groups acting on $Ł_m$ and $Ł_n^{\mathrm{R}}$ respectively. We prove a reduction theorem saying that, under certain conditions on $\g$, the local rings of the slices at $\g$ and $\n$ are …