相关论文: A tour of stable reduction with applications

We show that the locally free sheaf of locally exact differentials on a smooth projective curve of genus at least two over an algebraically closed field k of characteristic p is a stable vector bundle. This answers a question of Raynaud.

We introduce and study a notion of Castelnuovo-Mumford regularity suitable for rational normal scroll surfaces. In this setting we prove analogs of some classical properties. We prove splitting criteria for coherent sheaves and a…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

We introduce a new compactification of the space of relative stable maps. This new method uses logarithmic geoemtry in the sense of Kato-Fontaine-Illusie rather than the expanded degeneration. The underlying structure of our log stable maps…

For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…

In this paper we study the local geometry of the stack of pointed $A_r$-stable curves. In particular, we analyze the deformation theory of $A_r$-stable curves and their automorphism groups in order to study the combinatorics of families of…

We prove in this note a stabilized version of a conjecture on $\A^1$-connectedness. For the stabilized version of this conjecture, we introduce the notion of stable $\A^1$-connectedness, which is can be seen as the stabilization of…

We extend the results of Deligne and Illusie on liftings modulo $p^2$ and decompositions of the de Rham complex in several ways. We show that for a smooth scheme $X$ over a perfect field $k$ of characteristic $p>0$, the truncations of the…

Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…

We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along sequences of lattices in them, such as…

Suppose $Y$ is a smooth variety equipped with a top form. We prove a simple theorem giving a sharp lower bound on the geometric genus of a family of subvarieties of $Y$, in terms of the dimension of this family. Two elementary applications…

We characterise subcategories of semistable modules for noncommutative minimal models of compound Du Val singularities, including the non-isolated case. We find that the stability is controlled by an infinite polyhedral fan that stems from…

We give a description of the Deligne-Mumford properad expressing it as the result of homotopically trivializing S1 families of annuli (with appropriate compatibility conditions) in the properad of smooth Riemann surfaces with parameterized…

We define a notion of model for the $\lambda$$\Pi$-calculus modulo theory and prove a soundness theorem. We then define a notion of super-consistency and prove that proof reduction terminates in the $\lambda$$\Pi$-calculus modulo any…

We study the property of \emph{continuous Castelnuovo-Mumford regularity}, for semihomogeneous vector bundles over a given Abelian variety, which was formulated in \cite{Kuronya:Mustopa:2020} by K\"{u}ronya and Mustopa. Our main result…

We prove that the Gibbs states of classical, and commuting-Pauli, Hamiltonians are stable under weak local decoherence: i.e., we show that the effect of the decoherence can be locally reversed. In particular, our conclusions apply to…

We construct reduction and wall-crossing morphisms between the moduli spaces of stable pairs as the coefficients vary, generalizing the earlier work of Ascher, Bejleri, Inchiostro and Patakfalvi which deals with the klt case. Along the…

The purpose of this paper is to initiate a new attack on Arveson's resistant conjecture, that all graded submodules of the $d$-shift Hilbert module $H^2$ are essentially normal. We introduce the stable division property for modules (and…

From a certain strongly equivariant bundle gerbe with connection and curving over a smooth manifold on which a Lie group acts, we construct under some conditions a bundle gerbe with connection and curving over the quotient space. In…

For an arbitrary non-archimedean local field we classify reductive group schemes over the corresponding Fargues-Fontaine curve by group schemes over the category of isocrystals. We then classify torsors under such reductive group schemes by…