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  • Regularity of homogenized boundary data in periodic homogenization of elliptic systems
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-06-04
    Zhongwei Shen; Jinping Zhuge

    This paper is concerned with the periodic homogenization of second-order elliptic systems in divergence form with oscillating Dirichlet data or Neumann data of first order. We prove that the homogenized boundary data belongs to $W^{1, p}$ for any $1 < p < \infty$. In particular, this implies that the boundary layer tails are Hölder continuous of order $\alpha$ for any $\alpha \in (0,1)$.

    更新日期:2020-07-24
  • Abundance for 3-folds with non-trivial Albanese maps in positive characteristic
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-06-08
    Lei Zhang

    In this paper, we prove abundance for 3-folds with nontrivial Albanese maps, over an algebraically closed field of characteristic $p > 5$.

    更新日期:2020-07-24
  • Brauer trees of unipotent blocks
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-06-15
    David A. Craven; Olivier Dudas; Raphaël Rouquier

    In this paper we complete the determination of the Brauer trees of unipotent blocks (with cyclic defect groups) of finite groups of Lie type. These trees were conjectured by the first author in [19]. As a consequence, the Brauer trees of principal $\ell$-blocks of finite groups are known for $\ell > 71$.

    更新日期:2020-07-24
  • Homotopy finiteness of some DG categories from algebraic geometry
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-06-15
    Alexander I. Efimov

    In this paper, we prove that the bounded derived category $D^b_{\mathrm {coh}}(Y)$ of coherent sheaves on a separated scheme $Y$ of finite type over a field k of characteristic zero is homotopically finitely presented. This confirms a conjecture of Kontsevich. We actually prove a stronger statement: $D^b_{\mathrm {coh}}(Y)$ is equivalent to a DG quotient $D^b_{\mathrm {coh}}(\tilde{Y})/T,$ where $\tilde{Y}$

    更新日期:2020-07-24
  • L$^2$ well-posedness of boundary value problems for parabolic systems with measurable coefficients
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-06-15
    Pascal Auscher; Moritz Egert; Kaj Nyström

    We prove the first positive results concerning boundary value problems in the upper half-space for second order parabolic systems only assuming measurability and some transversal regularity in the coefficients of the elliptic part. To do so, we introduce and develop a first order strategy by means of a parabolic Dirac operator at the boundary to obtain, in particular, Green’s representation for solutions

    更新日期:2020-07-24
  • Degré de définition des endomorphismes d'une variété abélienne
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-06-22
    Gaël Rémond

    Given an abelian variety over a field of characteristic zero, we give an optimal explicit upper bound depending only on the dimension for the degree of the smallest extension of the base field over which all endomorphisms of the abelian variety are defined. For each dimension, the bound is achieved over the rationals by twisting a power of a CM elliptic curve. This complements a result of Guralnick

    更新日期:2020-07-24
  • Homology and homotopy complexity in negative curvature
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-05-11
    Uri Bader; Tsachik Gelander; Roman Sauer

    A classical theorem of Gromov states that the Betti numbers, i.e. the size of the free part of the homology groups, of negatively curved manifolds are bounded by the volume. We prove an analog of this theorem for the torsion part of the homology in all dimensions $d \neq 3$. Thus the total homology is controlled by the volume. This applies in particular to the classical case of hyperbolic manifolds

    更新日期:2020-07-20
  • Stability of valuations and Kollár components
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-05-11
    Chi Li; Chenyang Xu

    We prove that among all Kollár components obtained by plt blow ups of a klt singularity $o \in (X,D)$, there is at most one that is (log-)K-semistable. We achieve this by showing that if such a Kollár component exists, it uniquely minimizes the normalized volume function introduced in [Li18] among all divisorial valuations. Conversely, we show that any divisorial minimizer of the normalized volume

    更新日期:2020-07-20
  • Solidification of porous interfaces and disconnection
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-05-19
    Maximilian Nitzschner; Alain-Sol Sznitman

    In this article we obtain uniform estimates on the absorption of Brownian motion by porous interfaces surrounding a compact set. An important ingredient is the construction of certain resonance sets, which are hard to avoid for Brownian motion starting in the compact set. As an application of our results, we substantially strengthen the results of [22], and obtain when $d \geq 3$, large deviation upper

    更新日期:2020-07-20
  • Resolving Stanley's $e$-positivity of claw-contractible-free graphs
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-05-28
    Samantha Dahlberg; Angèle Foley; Stephanie van Willigenburg

    In Stanley’s seminal 1995 paper on the chromatic symmetric function, he stated that there was no known graph that was not contractible to the claw and whose chromatic symmetric function was not $e$-positive, that is, not a positive linear combination of elementary symmetric functions. We resolve this by giving infinite families of graphs that are not contractible to the claw and whose chromatic symmetric

    更新日期:2020-07-20
  • Bernstein–von Mises theorems for statistical inverse problems I: Schrödinger equation
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-05-28
    Richard Nickl

    The inverse problem of determining the unknown potential $f > 0$ in the partial differential equation $$\frac{\Delta}{2} u - fu =0 \: \mathrm{on} \mathcal O, \:\: u = g \mathrm{on} \partial \mathcal O,$$ where $\mathcal O$ is a bounded $C^\infty$-domain in $\mathbb R^d$ and $g > 0$ is a given source function, is considered. The data consist of the solution $u$ corrupted by additive Gaussian noise.

    更新日期:2020-07-20
  • Pushforwards of pluricanonical bundles under morphisms to abelian varieties
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-05-06
    Luigi Lombardi; Mihnea Popa; Christian Schnell

    Let $f \colon X \to A$ be a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). We show that the sheaves $f_{\ast} \omega_X^{\tensor m}$ become globally generated after pullback by an isogeny. We use this to deduce a decomposition theorem for these sheaves when $m \ge 2$, analogous to that obtained by Chen–Jiang when $m = 1$. This is in turn applied

    更新日期:2020-05-06
  • The Berenstein–Zelevinsky quantum cluster algebra conjecture
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-04-30
    Kenneth R. Goodearl; M. T. Yakimov

    We prove the Berenstein–Zelevinsky conjecture that the quantized coordinate rings of the double Bruhat cells of all finite-dimensional connected, simply connected simple algebraic groups admit quantum cluster algebra structures with initial seeds as specified by [5]. We furthermore prove that the corresponding upper quantum cluster algebras coincide with the constructed quantum cluster algebras and

    更新日期:2020-04-30
  • A proof of the Multijoints Conjecture and Carbery's generalization
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-04-17
    Ruixiang Zhang

    Given a set of lines in a $d$-dimensional linear space $\mathbb F^d$, a joint formed by them is a point lying on d given lines whose directions are linearly independent. The Joints Theorem gives a sharp upper bound of the total number of joints, up to a multiplicative constant. We present a new proof of the Joints Theorem without taking derivatives. Then we generalize our proof to prove the Multijoints

    更新日期:2020-04-17
  • Effective difference elimination and Nullstellensatz
    J. Eur. Math. Soc. (IF 2.19) Pub Date : 2020-04-17
    Alexey Ovchinnikov; Gleb Pogudin; Thomas Scanlon

    We prove effective Nullstellensatz and elimination theorems for difference equations in sequence rings. More precisely, we compute an explicit function of geometric quantities associated to a system of difference equations (and these geometric quantities may themselves be bounded by a function of the number of variables, the order of the equations, and the degrees of the equations) so that for any

    更新日期:2020-04-17
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