相关论文: A geometric Jacquet functor

In this note we compute length, support and dimension of syzygy modules of certain modules. This partially answers questions asked by Huneke et al.

In this PhD thesis, we give a new geometric approach to higher Teichm\"uller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The…

We utilize effective algorithms for computing in the cohomology of a Shimura curve together with the Jacquet-Langlands correspondence to compute systems of Hecke eigenvalues associated to Hilbert modular forms over a totally real field.

We determine the structure of the fibered biset functor sending a finite group $G$ to the complex vector space of complex valued class functions of $G$. Previously, it is studied as a biset functor by Bouc and as a $\mathbb…

I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.

In this note, we extend the quasi-projective dimension of finite (that is, finitely generated) modules to homologically finite complexes, and we investigate some of homological properties of this dimension.

In the 90's Soergel constructed a functor that relates Harish-Chandra bimodules to Soergel bimodules. We revisit this functor and relate it to the restriction functor constructed by Losev between Harish-Chandra bimodules and bimodules over…

We study some aspects of the geometric side of the Jacquet-Rallis relative trace formula. Globally, we compute each geometric term of the Jacquet-Rallis relative trace formula on the general linear group for regular supported test…

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results…

We give some functorial characterizations of flat strict Mittag-Leffler modules. We characterize reflexive functors of modules with similar tools, definitions and theorems.

For any complex reductive Lie algebra g and any locally finite g-module V, we extend to the tensor product of U(g) with V the Harish-Chandra description of g-invariants in the universal enveloping algebra U(g).

In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.

An interpretation of the Casselman-Wallach (C-W) Theorem is that the $K$-finite functor is an isomorphism of categories from the category of finitely generated, admissible smooth Fr\'echet modules of moderate growth to the category of…

We establish a criterion for determining when a family of geometric functors is jointly conservative through the lens of purity in compactly generated triangulated categories. We introduce the notion of pure descendability and we apply it…

We survey some basic geometric properties of the Funk metric of a convex set in $\mathbb{R}^n$. In particular, we study its geodesics, its topology, its metric balls, its convexity properties, its perpendicularity theory and its isometries.…

This note is devoted to the study of the links between the Hilbert function of a subscheme X of the projective space, and its geometric properties. We will assume that X is arithmetically Cohen-Macaulay, which allows us to characterize its…

We define geometric crystals and unipotent crystals for arbitrary Kac-Moody groups and describe geometric and unipotent crystal structures on the Schubert varieties.

Many properties of a module can be expressed in terms of the dimension of the vector space obtained by applying a finitely presented functor to that module. For example, the dimension of the kernel, image or cokernel of the multiplication…

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated…

It is characterized when coarsening functors between categories of graded modules preserve injectivity of objects, and when they commute with graded covariant Hom functors.