Related papers: Schematic Harder-Narasimhan Stratification
Let $K$ be a finite field extension of $Q_p$ and let $G_K$ be its absolute Galois group. We construct the universal family of filtered $(\phi,N)$-modules, or (more generally) the universal family of $(\phi,N)$-modules with a Hodge-Pink…
This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full…
In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…
The aim of this paper is to give a unified definition of a large class of discriminants arising in algebraic geometry using the discriminant of a morphism of locally free sheaves. The discriminant of a morphism of locally free sheaves has a…
Jun-Muk Hwang and Ngaiming Mok have proved the rigidity of irreducible Hermitian symmetric spaces of compact type under Kaehler degeneration. I adapt their argument to the algebraic setting in positive characteristic, where cominuscule…
We show that the cohomology of the structure sheaf of smooth and proper schemes over a complete non-archimedean field $K$ of characteristic zero, can be refined to an $\mathbf{A}^1$-invariant cohomology theory of smooth (not necessarily…
We construct a canonical stabilizer reduction $\widetilde{X}$ for any derived $1$-algebraic stack $X$ over $\mathbb{C}$ as a sequence of derived Kirwan blow-ups, under mild natural conditions that include the existence of a good moduli…
We study a notion of total acyclicity for complexes of flat sheaves over a scheme. It is Zariski-local - i.e. it can be verified on any open affine covering of the scheme - and it agrees, in their setting, with the notion studied by Murfet…
In this article we study chains of torsion classes in an abelian category $\mathcal{A}$. We prove that each chain of torsion classes induce a Harder-Narasimhan filtration for every nonzero object $M$ in $\mathcal{A}$, generalising a…
We study completely the Hilbert scheme and punctual Hilbert scheme of a nodal curve, and the relative Hilbert scheme of a family of curves acquiring a node. The results are then extended, less completely, to flag Hilbert schemes,…
In a recent paper, Colliot-Th\'el\`ene, Parimala and Suresh conjectured that a local-global principle holds for projective homogeneous spaces of connected linear algebraic groups over function fields of p-adic curves. In this paper, we show…
We introduce squared families, which are families of probability densities obtained by squaring a linear transformation of a statistic. Squared families are singular, however their singularity can easily be handled so that they form regular…
Let $M$ be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric $g$ and a covariant constant volume form. Let $G$ be either a connected reductive complex linear algebraic group or the real locus…
In this paper we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed curves to be…
One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by…
We display a symmetric monoidal equivalence between the stable $\infty$-category of filtered spectra, and quasi-coherent sheaves on $\mathbb{A}^1 / \mathbb{G}_m$, the quotient in the setting of spectral algebraic geometry, of the flat…
We revisit the Harder-Narasimhan stratification on a minuscule $p$-adic flag variety, by the theory of modifications of $G$-bundles on the Fargues-Fontaine curve. We compare the Harder-Narasimhan strata with the Newton strata introduced by…
Given a finite cocommutative Hopf algebra $A$ over a commutative regular ring $R$, the lattice of localising tensor ideals of the stable category of Gorenstein projective $A$-modules is described in terms of the corresponding lattices for…
This article settles the convergence question for multivariate barycentric subdivision schemes with nonnegative masks on complete metric spaces of nonpositive Alexandrov curvature, also known as Hadamard spaces. We establish a link between…
In characteristic zero, semistable principal bundles on a nonsingular projective curve with a semisimple structure group form a bounded family, as shown by Ramanathan in 1970's using the Narasimhan-Seshadri theorem. This was the first step…