Related papers: Generalized Motives through Witt Vectors
I study the modal theory of linear orders under embeddings, monotone maps, condensations, and end-extensions. I prove modality elimination for embeddings and monotone maps, show that condensations make scatteredness modally definable, and…
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.
We survey foundational principles of Grothendieck's generalized spaces, including a critical glossary of the various, and often conflicting, terminological usages. Known results using generalized points support a fully pointwise notation…
We study the rational Chow motives of certain moduli spaces of vector bundles on a smooth projective curve with additional structure (such as a parabolic structure or Higgs field). In the parabolic case, these moduli spaces depend on a…
The generalized sequence of numbers is defined by W_{n}=pW_{n-1}+qW_{n-2} with initial conditions W_{0}=a and W_{1}=b for a,b,p,q\inZ and n\geq2, respectively. Let W_{n}=circ(W_{1},W_{2},...,W_{n}). The aim of this paper is to establish…
Relying on recent advances in the theory of motives we develope a general formalism for derived categories of motives with Q-coefficients on perfect (ind-)schemes. As an application we give a motivic refinement of Zhu's geometric Satake…
Recently, we have witnessed the great success of the generalist model in natural language processing. The generalist model is a general framework trained with massive data and is able to process various downstream tasks simultaneously.…
This article is based on lecture notes prepared for the August 2006 Cologne Summer School. The first part contains background material and references for beginners. The second (and main) part is a survey of the current status in the theory…
The purpose of this this paper is to generalize the functors arising from the theory of Witt vectors duto to Cartier. Given a polynomial $g(q)\in \mathbb Z[q]$, we construct a functor ${\overline {W}}^{g(q)}$ from the category of $\mathbb…
Let $X$ be a smooth projective surface with a full strong exceptional sequence $\mathfrak{E}$. Under certain conditions, we describe the moduli spaces of framed sheaves on a line in $X$ via linear data, i.e. by realizing them as principal…
From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the…
The main goal of the paper is to present a new approach via Hurwitz numbers to Kontsevich's combinatorial/matrix model for the intersection theory of the moduli space of curves. A secondary goal is to present an exposition of the circle of…
We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger-Murre and Corti-Hanamura. We first obtain a general motivic decomposition for the Chow motive of an arbitrary…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
We develop a notion of exponential motives on general prestacks equipped with a $\mathbf{G}_a$-action, and compare them with Whittaker motives via Gaitsgory's Kirillov model. We then establish foundational results for exponential motives on…
In this paper, a generalized cusp is a properly convex manifold with strictly convex boundary that is diffeomorphic to $M \times [0, \infty)$ where $M$ is a closed Euclidean manifold. These are classified in [2]. The marked moduli space is…
Let $R$ be a commutative unital ring, $a\in R$ and $t$ a positive integer. $a^{t}$-reduced $R$-modules and universally $a^{t}$-reduced $R$-modules are defined and their properties given. Known (resp. new) results about reduced $R$-modules…
We study vector bundles on curves with rational tails and their smoothings and give a sufficient condition for the general fibre to be balanced.
Comtraces (combined traces) are extensions of Mazurkiewicz traces that can model the "not later than" relationship. In this paper, we first introduce the novel notion of generalized comtraces, extensions of comtraces that can additionally…