Related papers: The relative minimal model program for excellent a…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

If $V$ is an equidimensional codimension $c$ subscheme of an $n$-dimensional projective space, and $V$ is linked to $V'$ by a complete intersection $X$, then we say that $V$ is {\em minimally linked} to $V'$ if $X$ is a codimension $c$…

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact $p$-adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In…

We show the validity of the relative dlt MMP over Q-factorial threefolds in all characteristics p>0. As a corollary, we generalise many recent results to low characteristics including: $W\mathcal{O}$-rationality of klt singularities,…

The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…

We characterize the variety of compatible fundamental matrix triples by computing its multidegree and multihomogeneous vanishing ideal. This answers the first interesting case of a question recently posed by Br{\aa}telund and Rydell. Our…

With a grading previously introduced by the second-named author, the multiplication maps in the preprojective algebra satisfy a maximal rank property that is similar to the maximal rank property proven by Hochster and Laksov for the…

A standard tool for classifying the complexity of equivalence relations on $\omega$ is provided by computable reducibility. This reducibility gives rise to a rich degree structure. The paper studies equivalence relations, which induce…

We present a non-standard proof of the fact that the existence of a local (i.e. restricted to a point) characteristic-zero, semi-parametric lifting for a variety defined by the zero locus of polynomial equations over the integers is…

First, we prove an algebraization result for rig-smooth algebras over a general noetherian ring; this positively answers the question raised in [Sta24, Tag 0GAX]. Then we prove a general partial algebraization result in non-archimedean…

This paper aims at developing a "local--global" approach for various types of finite dimensional algebras, especially those related to Hecke algebras. The eventual intention is to apply the methods and applications developed here to the…

We classify group schemes in terms of their Cartier modules. We also prove the equivalence of different definitions of the tangent space and the dimension for these group schemes; in particular, the minimal dimension of a formal group law…

We generalize the higher Riemann-Hilbert correspondence in the presence of scalar curvature for a (possibly non-compact) smooth manifold $M$. We show that the dg-category of curved $\infty$-local systems, the dg-category of graded vector…

The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in…

This is the second of a series of papers studying real algebraic threefolds using the minimal model program. The main result is the following. Let $X$ be a smooth projective real algebraic 3-fold. Assume that the set of real points is an…

This is the first in a series of two papers concerned with relative birational geometry of algebraic spaces. In this paper, we study Pr\"ufer spaces and Pr\"ufer pairs of algebraic spaces that generalize spectra of Pr\"ufer rings. As a…

For a fixed constant $\lambda > 0$ and a bounded Lipschitz domain $\Omega \subset \mathbb{R}^n$ with $n \geq 2$, we establish that almost-minimizers (functions satisfying a sort of variational inequality) of the Alt-Caffarelli type…

This paper studies finitely generated quasivarieties of Sugihara algebras. These quasivarieties provide complete algebraic semantics for certain propositional logics associated with the relevant logic R-mingle. The motivation for the paper…

The ascent and descent of the Mittag-Leffler property were instrumental in proving Zariski locality of the notion of an (infinite dimensional) vector bundle by Raynaud and Gruson in \cite{RG}. More recently, relative Mittag-Leffler modules…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…