In [31] we defined a regularized analytic torsion for quotients of the symmetric space $\operatorname{SL}(n,\mathbb{R})/\operatorname{SO}(n)$ by arithmetic lattices. In this paper we study the limiting behavior of the analytic torsion as the lattices run through sequences of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for principal congruence subgroups and strongly

We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for $\mathit{GSp}_{4}/\mathbb{Q}$ in various aspects. A main tool is Arthur’s invariant trace formula. While Shin [Automorphic Plancherel density theorem, Israel J. Math.192(1) (2012), 83–120] and Shin–Templier [Sato–Tate theorem for families and low-lying zeros of automorphic $L$ -functions, Invent. Math.203(1) (2016)

We extend T. Y. Thomas’s approach to projective structures, over the complex analytic category, by involving the $\unicode[STIX]{x1D70C}$ -connections. This way, a better control of projective flatness is obtained and, consequently, we have, for example, the following application: if the twistor space of a quaternionic manifold $P$ is endowed with a complex projective structure then $P$ can be locally

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over  $\overline{\mathbb{F}}_{p}$ of parallel weight 1 and level prime to $p$ is unramified above  $p$ . This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight 1. The proof is based on the observation that parallel

Let $q$ be an anisotropic quadratic form defined over a general field $F$ . In this article, we formulate a new upper bound for the isotropy index of $q$ after scalar extension to the function field of an arbitrary quadric. On the one hand, this bound offers a refinement of an important bound established in earlier work of Karpenko–Merkurjev and Totaro; on the other hand, it is a direct generalization

We study the germs at the origin of $G$ -representation varieties and the degree 1 cohomology jump loci of fundamental groups of quasi-projective manifolds. Using the Morgan–Dupont model associated to a convenient compactification of such a manifold, we relate these germs to those of their infinitesimal counterparts, defined in terms of flat connections on those models. When the linear algebraic group

In this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique) $L_{\infty }$ space. More precisely, we construct a faithful functor from the category of Lie algebroids to the category of $L_{\infty }$ spaces. Then we show that for each Lie algebroid

Let $G$ be a semisimple Lie group with associated symmetric space $D$ , and let $\unicode[STIX]{x1D6E4}\subset G$ be a cocompact arithmetic group. Let $\mathscr{L}$ be a lattice inside a $\mathbb{Z}\unicode[STIX]{x1D6E4}$ -module arising from a rational finite-dimensional complex representation of $G$ . Bergeron and Venkatesh recently gave a precise conjecture about the growth of the order of the torsion

Subconvexity bounds on the critical line are proved for general Epstein zeta-functions of $k$ -ary quadratic forms. This is related to sup-norm bounds for unitary Eisenstein series on $\text{GL}(k)$ associated with the maximal parabolic of type $(k-1,1)$ , and the exact sup-norm exponent is determined to be $(k-2)/8$ for $k\geqslant 4$ . In particular, if $k$ is odd, this exponent is not in $\frac{1}{4}\mathbb{Z}$

We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface $\unicode[STIX]{x1D6F4}$ . As a corollary we obtain a new convergence result for sequences of metrics with conical singularities, where an accumulation of singularities is allowed.

In this paper, we study the singularities of a general hyperplane section $H$ of a three-dimensional quasi-projective variety $X$ over an algebraically closed field of characteristic $p>0$ . We prove that if $X$ has only canonical singularities, then $H$ has only rational double points. We also prove, under the assumption that $p>5$ , that if $X$ has only klt singularities, then so does $H$ .

None

None

Nous construisons un espace adapté à l’étude de l’entropie des applications méromorphes en utilisant des limites projectives. Nous en déduisons un principe variationnel pour ces applications.

We develop a theory of $R$ -module Thom spectra for a commutative symmetric ring spectrum $R$ and we analyze their multiplicative properties. As an interesting source of examples, we show that $R$ -algebra Thom spectra associated to the special unitary groups can be described in terms of quotient constructions on $R$ . We apply the general theory to obtain a description of the $R$ -based topological

Let $\unicode[STIX]{x1D707}$ be the projection on $[0,1]$ of a Gibbs measure on $\unicode[STIX]{x1D6F4}=\{0,1\}^{\mathbb{N}}$ (or more generally a Gibbs capacity) associated with a Hölder potential. The thermodynamic and multifractal properties of $\unicode[STIX]{x1D707}$ are well known to be linked via the multifractal formalism. We study the impact of a random sampling procedure on this structure

Two measurable sets $S,\unicode[STIX]{x1D6EC}\subseteq \mathbb{R}^{d}$ form a Heisenberg uniqueness pair, if every bounded measure $\unicode[STIX]{x1D707}$ with support in $S$ whose Fourier transform vanishes on $\unicode[STIX]{x1D6EC}$ must be zero. We show that a quadratic hypersurface and the union of two hyperplanes in general position form a Heisenberg uniqueness pair in $\mathbb{R}^{d}$ . As

Estimating averages of Dirichlet convolutions $1\ast \unicode[STIX]{x1D712}$ , for some real Dirichlet character $\unicode[STIX]{x1D712}$ of fixed modulus, over the sparse set of values of binary forms defined over $\mathbb{Z}$ has been the focus of extensive investigations in recent years, with spectacular applications to Manin’s conjecture for Châtelet surfaces. We introduce a far-reaching generalisation

Colmez [Périodes des variétés abéliennes a multiplication complexe, Ann. of Math. (2)138(3) (1993), 625–683; available at http://www.math.jussieu.fr/∼colmez] conjectured a product formula for periods of abelian varieties over number fields with complex multiplication and proved it in some cases. His conjecture is equivalent to a formula for the Faltings height of CM abelian varieties in terms of the

In this paper, we construct the first examples of complex surfaces of general type with arbitrarily large geometric genus whose canonical maps induce non-hyperelliptic fibrations of genus $g=4$ , and on the other hand, we prove that there is no complex surface of general type whose canonical map induces a hyperelliptic fibrations of genus $g\geqslant 4$ if the geometric genus is large.

In this paper, we consider the Stokes equations in a perforated domain. When the number of holes increases while their radius tends to 0, it is proven in Desvillettes et al. [J. Stat. Phys. 131 (2008) 941–967], under suitable dilution assumptions, that the solution is well approximated asymptotically by solving a Stokes–Brinkman equation. We provide here quantitative estimates in $L^{p}$ -norms of

We present a construction that enables one to find Banach spaces $X$ whose sets $\operatorname{NA}(X)$ of norm attaining functionals do not contain two-dimensional subspaces and such that, consequently, $X$ does not contain proximinal subspaces of finite codimension greater than one, extending the results recently provided by Read [Banach spaces with no proximinal subspaces of codimension 2, Israel

None

None