Related papers: Quasi-Projective Moduli for Polarized klt Good Min…

Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with respect to the parameter. When the foliation is of general type,…

We develop some results on the positivity of direct image bundles in the particular case of a trivial fibration over a one-dimensional base. We also apply the results to study variations of Kahler metrics.

Let $F$ be a locally compact non-Archimedean field, and $\bf G$ a connected quasi-split reductive group over $F$. We are interested in complex irreducible smooth generic representations $\pi$ of ${\bf G}(F)$. When $F$ has positive…

We construct a local deformation problem for residual Galois representations $\bar{\rho}$ valued in an arbitrary reductive group $\hat{G}$ which we use to develop a variant of the Taylor-Wiles method. Our generalization allows Taylor-Wiles…

Suppose $G$ is a connected noncompact locally compact group, $A,B$ are nonempty and compact subsets of $G$, $\mu$ is a left Haar measure on $G$. Assuming that $G$ is unimodular, and $ \mu(A^2) < K \mu(A) $ with $K>1$ a fixed constant, our…

Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. Let $d\in H_2(X)$ be a…

We prove a version of Jonsson-Musta\c{t}\v{a}'s Conjecture, which says for any graded sequence of ideals, there exists a quasi-monomial valuation computing its log canonical threshold. As a corollary, we confirm Chi Li's conjecture that a…

We address two questions related to the semiampleness of line bundles arising from Hodge theory. First, we prove there is a functorial compactification of the image of a period map of a polarizable integral pure variation of Hodge…

We show that for quasi-compact quasi-separated schemes of finite dimension, the constructibility condition in real \'etale cohomology agrees with a notion of constructibility arising naturally from topology. As application we prove that the…

We introduce a general formalism with minimal requirements under which we are able to prove the pro-modular Fontaine-Mazur conjecture. We verify it in the ordinary case using the recent construction of Breuil and Herzig.

Let $G$ be a simply-connected semisimple algebraic group scheme over an algebraically closed field of characteristic $p > 0$. Let $r \geq 1$ and set $q = p^r$. We show that if a rational $G$-module $M$ is projective over the $r$-th…

We consider the 2D quasi-geostrophic model and its two different regularizations. Global regularity results are established for the regularized models with subcritical or critical indices. The proof of Onsager's conjecture concerning weak…

We establish a local rigidity theorem for quasi--Lie brackets on quaternionic Banach right modules. Under quantitative control of antisymmetry and Jacobi defects, we construct an explicit bilinear correction that preserves right…

In an earlier paper we showed that we can improve results by Emmy Noether and Alexander Ostrowski concerning the reducibility modulo p of absolutely irreducible polynomials with integer coefficients by giving the problem a geometric turn…

We show the properness of the moduli stack of stable surfaces over $\mathbb{Z}[1/30]$, assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local Kawamata--Viehweg vanishing theorem for for 3-dimensional…

We study quasiconformal mappings in planar domains $\Omega$ and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the…

In this paper, we prove the Kobayashi hyperbolicity of the coarse moduli spaces of canonically polarized or polarized Calabi-Yau manifolds in the sense of complex $V$-spaces (a generalization of complex $V$-manifolds in the sense of…

For $\mathbb Q$-factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we deduce the existence of the minimal model program for such…

We characterize projective and injective Banach modules in approximate terms, generalizing thereby a characterization of contractible Banach algebras given by F. Ghahramani and R. J. Loy. As a corollary, we show that each uniformly…

Given a sequence of genus $g\geq 2$ curves converging to a punctured Riemann surface with complete metric of constant Gaussian curvature $-1$. we prove that the Kodaira embedding using orthonormal basis of the Bergman space of sections of a…