相关论文: Vector bundles and p-adic representations I

In their paper Scholze and Weinstein show that a certain diagram of perfectoid spaces is Cartesian. In this paper, we generalize their result. This generalization will be used in a forthcoming paper of ours to compute certain non-trivial…

VB-groupoids are vector bundles in the category of Lie groupoids. They encompass several classical objects, including Lie group representations and 2-vector spaces. Moreover, they provide geometric pictures for 2-term representations up to…

We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.

We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of…

Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.

In this paper we introduce the notion of a geometric associative r-matrix attached to a genus one fibration with a section and irreducible fibres. It allows us to study degenerations of solutions of the classical Yang-Baxter equation using…

A tangent category is a category equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of the tangent bundle functor from classical differential geometry. Cockett and Cruttwell introduced…

We establish a valuative version of Grothendieck's section conjecture for curves over p-adic local fields. The image of every section is contained in the decomposition subgroup of a valuation which prolongs the p-adic valuation to the…

In this paper we consider the problem of pointwise determining the fibres of the flat unitary subbundle of a PVHS of weight one. Starting from the associated Higgs field, and assuming the base has dimension $1$, we construct a family of…

We study Picard groups and Picard functors of perfectoid spaces which are limits of rigid spaces. For sufficiently large covers that are limits of rigid spaces of good reduction, we show that the Picard functor can be represented by the…

We study aspects of the A^1-homotopy classification problem in dimensions >= 3 and, to this end, we investigate the problem of computing A^1-homotopy groups of some A^1-connected smooth varieties of dimension >=. Using these computations,…

Let $\mathcal{X} \subset \mathbb{P}_k^d$ be Drinfeld's halfspace over a finite field $k$ and let $\mathcal{E}$ be a homogeneous vector bundle on $\mathbb{P}_k^d$. The paper deals with two different descriptions of the space of global…

We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.

In this paper we characterize the fiber representations of equivariant complex vector bundles over a circle and classify these bundles. We also treat the triviality of equivariant complex vector bundles over a circle by investigating the…

In this article we describe vector bundles over projectivoid line and show how it is similar to (and different) from Gorthendieck's classification of vector bundles over projective line.

For any smooth proper rigid space $X$ over a complete algebraically closed extension $K$ of $\mathbb Q_p$ we give a geometrisation of the $p$-adic Simpson correspondence of rank one in terms of analytic moduli spaces: The $p$-adic character…

The toric fundamental group is the Tannaka dual of a category of vector bundles which become direct sums of line bundles on a finite \'etale cover. It is an extension of the \'etale fundamental group scheme by a projective limit of tori.…

Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections…

We present a geometric interpretation of tight closure in terms of vector bundles and projective bundles.