Related papers: Generalized Motives through Witt Vectors
In this note, using Borger's theory of periodic Witt vectors, we construct integral refinements of the arithmetic subalgebras associated with Bost-Connes systems for general number fields.
Foundation models have received much attention due to their effectiveness across a broad range of downstream applications. Though there is a big convergence in terms of architecture, most pretrained models are typically still developed for…
In a previous paper we have constructed a compactification $KGl_n$ of the general linear group $Gl_n$, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De…
We study the characterization and computation of general policies for families of problems that share a structure characterized by a common reduction into a single abstract problem. Policies $\mu$ that solve the abstract problem P have been…
A major challenge in research involving artificial intelligence (AI) is the development of algorithms that can find solutions to problems that can generalize to different environments and tasks. Unlike AI, humans are adept at finding…
We compute the motive of the classifying stack of an orthogonal group in the Grothendieck ring of stacks over a field of characteristic different from two.
We give a brief overview of recent progress in understanding Bagger-Witten line bundles, which are bundles over moduli spaces of two-dimensional N=2 SCFTs whose existence is a consequence of the global U(1)_R symmetry of the theories. Our…
We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop…
The convergence of a new general variable metric algorithm based on compositions of averaged operators is established. Applications to monotone operator splitting are presented.
We give the first examples of finite groups G such that the Chow ring of the classifying space BG depends on the base field, even for fields containing the algebraic closure of Q. As a tool, we give several characterizations of the…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
The goal of this paper is to show that Stokes data coming from flat bundles form a locally geometric derived stack locally of finite presentation. This generalizes existing geometricity results on Stokes data in four different directions:…
Graded vector bundles over a given $\mathbb{Z}$-graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base graded manifold, finitely generated projective graded modules…
Generalized planning is concerned with the characterization and computation of plans that solve many instances at once. In the standard formulation, a generalized plan is a mapping from feature or observation histories into actions,…
We introduce the notion of a generalized intersection pairing for an Artin stack with a proper good moduli space and nonempty stable part. For the moduli stack of semistable bundles over a smooth projective curve, there are four known…
We consider global generation of sheaves of coinvariants on the moduli space of curves given by simple modules over certain vertex operator algebras, extending results for affine VOAs at integrable levels on stable pointed rational curves.…
We prove a factorization theorem of generalized functions for moduli spaces of semistable parabolic bundles of any rank.
The power of neural networks lies in their ability to generalize to unseen data, yet the underlying reasons for this phenomenon remain elusive. Numerous rigorous attempts have been made to explain generalization, but available bounds are…
We consider learning from labeled data collected across multiple environments, where the data distribution may vary across these environments. This problem is commonly approached from a causal perspective, seeking invariant representations…
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…