Mathematische Annalen最新文献

For a prime number (p>2) and a finite extension (F/mathbb {Q}_p), we explain the construction of the difference divisors on the unitary Rapoport–Zink spaces of hyperspecial level over (mathcal {O}_{breve{F}}), and the GSpin Rapoport–Zink spaces of hyperspecial level over (breve{mathbb {Z}}_{p}) associated to a minuscule cocharacter (mu ) and a basic element b. We prove the regularity of the difference divisors, find the formally smooth locus of both the special cycles and the difference divisors, by a purely deformation-theoretic approach.

The purpose of this article is to study Newton polygons of certain abelian L-functions on curves. Let X be a smooth affine curve over a finite field (mathbb {F}_q) and let (rho :pi _1(X) rightarrow mathbb {C}_p^times ) be a finite character of order (p^n). By previous work of the first author, the Newton polygon ({{,mathrm{text {NP}},}}(rho )) lies above a ‘Hodge polygon’ ({{,mathrm{text {HP}},}}(rho )) defined using ramification invariants of (rho ). In this article we study the contact between these two polygons. We prove that ({{,mathrm{text {NP}},}}(rho )) and ({{,mathrm{text {HP}},}}(rho )) share a vertex if and only if a corresponding vertex is shared between the Newton and Hodge polygons of ‘local’ L-functions associated to each ramified point of (rho ). As a consequence, we determine a necessary and sufficient condition for the coincidence of ({{,mathrm{text {NP}},}}(rho )) and ({{,mathrm{text {HP}},}}(rho )).

In this paper, we prove that a non-projective compact Kähler three-fold with nef anti-canonical bundle is, up to a finite étale cover, one of the following: a manifold with vanishing first Chern class; the product of a K3 surface and the projective line; or a projective space bundle over a two-dimensional torus. This result extends Cao–Höring’s structure theorem for projective manifolds to compact Kähler manifolds in dimension 3. For the proof, we investigate the Minimal Model Program for compact Kähler three-folds with nef anti-canonical bundles by using the positivity of direct image sheaves, (mathbb {Q})-conic bundles, and orbifold vector bundles.

We prove boundedness, Hölder continuity, Harnack inequality results for local quasiminima to elliptic double phase problems of p-Laplace type in the general context of metric measure spaces. The proofs follow a variational approach and they are based on the De Giorgi method, a careful phase analysis and estimates in the intrinsic geometries.

We consider some algebraic aspects of the dynamics of an automorphism on a family of polarized abelian varieties parameterized by the complex unit disk. When the action on the cohomology of the generic fiber has no cyclotomic factor, we prove that such a map can be made regular only if the family of abelian varieties does not degenerate. As a contrast, we show that families of translations are always regularizable. We further describe the closure of the orbits of such maps, inspired by results of Cantat and Amerik–Verbitsky.

We give Martin representation of nonnegative functions caloric with respect to the fractional Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean value property for the space-time isotropic (alpha )-stable Lévy process. To derive the representation, we first establish the existence of the parabolic Martin kernel. This involves proving new boundary regularity results for both the fractional heat equation and the fractional Poisson equation with Dirichlet exterior conditions. Specifically, we demonstrate that the ratio of the solution and the Green function is Hölder continuous up to the boundary.

This paper generalizes D. Burago and S. Ivanov’s work (Duke Math J 162:1205–1248, 2013) on filling volume minimality and boundary rigidity of almost real hyperbolic metrics. We show that regions with metrics close to a negatively curved symmetric metric are strict minimal fillings and hence boundary rigid. This includes perturbations of complex, quaternionic and Cayley hyperbolic metrics.

If U is a (C^{infty }) function with compact support in the plane, we let u be its restriction to the unit circle ({mathbb {S}}), and denote by (U_i,,U_e) the harmonic extensions of u respectively in the interior and the exterior of ({mathbb {S}}) on the Riemann sphere. About a hundred years ago, Douglas [9] has shown that

thus giving three ways to express the Dirichlet norm of u. On a rectifiable Jordan curve (Gamma ) we have obvious analogues of these three expressions, which will of course not be equal in general. The main goal of this paper is to show that these 3 (semi-)norms are equivalent if and only if (Gamma ) is a chord-arc curve.

In this paper we show that if a compact set (E subset {mathbb {R}}^d), (d ge 3), has Hausdorff dimension greater than (frac{(4k-1)}{4k}d+frac{1}{4}) when (3 le d<frac{k(k+3)}{(k-1)}) or (d- frac{1}{k-1}) when (frac{k(k+3)}{(k-1)} le d), then the set of congruence class of simplices with vertices in E has nonempty interior. By set of congruence class of simplices with vertices in E we mean

where (2 le k <d). This result improves the previous best results in the sense that we now can obtain a Hausdorff dimension threshold which allow us to guarantee that the set of congruence class of triangles formed by triples of points of E has nonempty interior when (d=3) as well as extending to all simplices. The present work can be thought of as an extension of the Mattila–Sjölin theorem which establishes a non-empty interior for the distance set instead of the set of congruence classes of simplices.

Non-compact hyperkähler spaces arise frequently in gauge theory. The 4-dimensional hyperkähler ALE spaces are a special class of complete non-compact hyperkähler spaces. They are in one-to-one correspondence with the finite subgroups of SU(2) and have interesting connections with representation theory and singularity theory, captured by the McKay Correspondence. The 4-dimensional hyperkähler ALE spaces are first classified by Peter Kronheimer via a finite-dimensional hyperkähler reduction. In this paper, we give a new gauge-theoretic construction of these spaces. More specifically, we realize each 4-dimensional hyperkähler ALE space as a moduli space of solutions to a system of equations for a pair consisting of a connection and a section of a vector bundle over an orbifold Riemann surface, modulo a gauge group action. The construction given in this paper parallels Kronheimer’s original construction and hence can also be thought of as a gauge-theoretic interpretation of Kronheimer’s construction of these spaces.