arXiv subjects
Publications and source records attributed to Andrea Conti.
We prove a lower bound on the Weil height, the so-called Bogomolov property, for the algebraic extensions of $\mathbb Q$ cut out by the adelic Galois representations attached to certain eigenforms whose local component at a prime $p$ is supercuspidal. To this end, we give a method for constructing metric inequalities over $p$-adic Lie extensions of fields over $\mathbb Q$ that are finitely ramified at $p$.
We study small points in radical extensions of algebraic fields. Given an algebraic extension $\mathbb{F}$ of $\mathbb{Q}$, a finitely generated subgroup $Γ\subseteq \mathbb{F}^\times$, and a rational prime $p$, we give a general criterion ensuring that $\mathbb{F}(Γ^{p-\mathrm{div}})\setminus Γ^{\mathrm{div}}$ has the Bogomolov property. This problem is motivated by a conjecture of Rémond, formulated when $\mathbb{F}$ is a number field, predicting that such radical extensions contain no unexpected small points outside the divisible hull of the group used to generate them. As applications, we obtain new cases of Rémond's conjecture for radical extensions generated by division points with respect to a finite set of primes, recovering and extending previous results of Amoroso and the third author. Our argument is based on a recent result on small points in $p$-adic Lie extensions.
For a profinite group $G$ and a rigid analytic space $X$, we study when an $\mathcal O_X(X)$-linear representation $V$ of $G$ admits a lattice, i.e. an $\mathcal O_{\mathcal X(\mathcal X)}$-linear model for a suitable formal model $\mathcal X$ of $X$ in the sense of Berthelot. We give a positive answer, under mild assumptions, when $X$ is strictly quasi-Stein and regular. As a consequence, we are able to describe explicit open rational subdomains of $X$ over which $V$ is constant after reduction modulo a power of $p$. We give applications in two different directions. First, we prove explicit results on the reduction modulo powers of $p$ of sheaves of crystalline and semistable representations of fixed weight. Second, we deduce a result on the pseudorepresentation carried by the Coleman--Mazur eigencurve, which can be made explicit whenever equations for a rational subdomain of the eigencurve are given.
We study the trianguline variety for split connected reductive groups. We generalize a theorem of Breuil, Hellmann, and Schraen about its local structure, establishing smoothness over the loci determined by various regularity conditions on the triangulation parameter, and normality at certain points outside of these smooth loci. Along the way, we prove a crystallinity criterion for $(φ,Γ_K)$-modules with $\mathsf G$-structure.
We construct and study the supersymmetry properties of the weighted projective spaces $\mathbb{WCP}^2$ and $\mathbb{WCP}^3$. These are topologically $\mathbb{CP}^n$ with $n+1$ orbifold singularities and as such are higher dimensional analogues of the ``spindle'' or $\mathbb{WCP}^1$. We use these to construct interesting supersymmetric orbifolds of canonical near horizon geometries of relevance to the AdS/CFT correspondence. Interestingly, for certain tunings of their integer weights, and unlike the spindle, $\mathbb{WCP}^{2}$ and $\mathbb{WCP}^{3}$ are compatible with supersymmetry beyond the realm of gauged supergravity. This allows one to construct interesting supersymmetric solutions in type II supergravity such as AdS$_5\times\mathbb{WCP}^{2}\times\text{S}^1$ and AdS$_4\times \mathbb{WCP}^3$ via duality, in which $\mathbb{WCP}^n$ appears without a connection fibred over it. We also leverage our results to construct a supersymmetric AdS$_3$ solution containing a topological $\mathbb{T}^{(1,1)}$ space with 4 orbifold singularities.
We classify AdS$_3$ solutions of the U(1) invariant sector of minimal $d=7$ supergravity. We find two classes of solutions preserving ${\cal N}=(2,0)$ supersymmetry for which the internal space M$_4$ is either a negative curvature Kahler-Einstein manifold or a circle fibration over $Σ\times \mathbb{R}$. For the later, in the case that $Σ$ has constant curvature, we reduce finding a solution to solving a single ODE that admits polynomial solutions. Among these are interesting solutions whose uplifts to $d=11$ describe M5 branes wrapping various $d=4$ orbifolds. These include a topological $\mathbb{CP}^2$ with 2 orbifold fixed points that we identify as the weighted projective space $\mathbb{WCP}^2_{[k,k,\ell]}$. We are also able to construct solutions with M5 branes that wrap a spindle fibred over constant curvature Riemann surfaces of arbitrary genus. Such solutions should provide holographic duals to the ${\cal N}=(2,0)$ SCFT associated to the M5 brane compactified to $d=2$ on these orbifolds. We match the holographic central charges of these solutions to a field theory computation in terms of anomaly polynomials and c-extremisation.
We study three Type II supergravity solutions holographically dual to codimension-2 supersymmetric defects in $(p+1)$-dimensional SU($N$) maximally supersymmetric Yang-Mills theory ($p=2,3,4$). In all of these cases, the defects have a non-trivial monodromy for the maximal abelian subgroup for the SO($9-p$) R-symmetry. Such solutions are obtained by considering branes wrapping spindle configurations, changing the parameters (which alters the coordinate domain), and imposing suitable boundary conditions. We provide a prescription to compute the entanglement entropy of the effective theory on the defect. We find the resulting quantity to be proportional to the free energy of the ambient theory. A similar analysis is performed for the D5-brane wrapping a spindle, but we find that changing the coordinate domain does not lead to a defect solution, but rather to a circle compactification.
Water adsorption on silicate surfaces is a critical yet poorly understood process relevant to, e.g., mineral weathering and cement hydration. This study investigates the structure of water overlayers on a model calcium silicate, the lowest-energy (100) surface of wollastonite (CaSiO3). It combines atomically resolved non-contact atomic force microscopy (nc-AFM), acquired with qPlus sensors and functionalized tips in ultrahigh vacuum (UHV), with density functional theory (DFT) calculations employing the metaGGA r2SCAN+rVV10 functional. Adding incremental doses of water to the sample at cryogenic temperatures produces distinct structures governed by the competition between water-surface and water-water interactions. With two water molecules per surface unit cell, water-surface interactions dominate: In line with previous theoretical predictions, adsorbates follow the surface lattice. As the coverage increases, intermolecular hydrogen bonding competes with bonding to the surface, leading to the emergence of complex, coexisting patterns. While their small energy differences prevent an unambiguous identification of the most stable structure by DFT, the experimentally observed symmetries help constrain plausible structural models. Above a critical density of four water molecules per unit cell, water-water interactions prevail, and water clusters are formed. The results provide an atomic-scale framework for understanding water interactions with calcium silicate surfaces.
Alumina (Al$_{2}$O$_{3}$) is a key material for thin-film growth and heterogeneous catalysis, where the atomic surface structure critically impacts performance. Using noncontact atomic force microscopy (nc-AFM) combined with density functional theory (DFT) calculations, we challenge the common assumption that the unreconstructed $α$-Al$_{2}$O$_{3}$(0001) surface is atomically flat and uniformly Al-terminated. This widely accepted bulk termination satisfies polarity compensation requirements but results in highly undercoordinated surface Al cations at the surface. Despite substantial inward relaxation of these Al cations, we find that the (1 ${\times}$ 1) surface remains inherently metastable, relative to the thermodynamically stable $(\sqrt{31} \times \sqrt{31})R\pm9°$ surface reconstruction that forms at high temperatures above 1000 °C. Nc-AFM imaging of the unreconstructed surface reveals a rough and disordered morphology, with only nanometer-scale regions exhibiting the ordered Al-terminated (1 $\times$ 1) structure. Our results show that the unreconstructed Al$_{2}$O$_{3}$(0001) surface is intrinsically inhomogeneous, reconciling conflicting experimental observations and challenging the validity of commonly used atomistic models.
Let $Γ$ be either i) the absolute Galois group of a local field $F$, or ii) the topological fundamental group of a closed connected orientable surface of genus $g$. In case i), assume that $μ_{p^2} \subset F$. We give an elementary and unified proof that every representation $ρ_1: Γ\to \mathbf{GL}_d(\mathbb{F}_p)$ lifts to a representation $ρ_2: Γ\to \mathbf{GL}_d(\mathbb{Z}/p^2)$. [In case i), it is understood these are continuous.] The actual statement is much stronger: for all $r \geq 1$, under "suitable" assumptions, triangular representations $ρ_r: Γ\to \mathbf{B}_d(\mathbb{Z}/p^r)$ lift to $ρ_{r+1}: Γ\to \mathbf{B}_d(\mathbb{Z}/p^{r+1})$, in the strongest possible step-by-step sense. Here "suitable" is made precise by the concept of $\textit{Kummer flag}$. An essential aspect of this work is to identify the common properties of groups i) and ii) that suffice to ensure the existence of such lifts.
We study congruences modulo powers of a prime $p$ between pairs of $p$-new modular Hecke eigenforms of level $Γ_0(p)$ and same weight $k$. Based on explicit computations, we conjecture that every such eigenform $f$ admits a twin to which it is congruent modulo a surprisingly high power of $p$, whose exponent is close to the opposite of the valuation of the $\mathcal L$-invariant of $f$, and whose Atkin--Lehner sign is opposite to that of $f$. This is a new phenomenon that is not explained by the known results on the $p$-adic variation of eigenforms. Inspired by the global picture, we formulate a local conjecture describing congruences between semistable representations of fixed weight, varying $\mathcal L$-invariant, and opposite Atkin--Lehner signs. We give some theoretical evidence towards our conjectures.
The estimation of the Risk Neutral Density (RND) implicit in option prices is challenging, especially in illiquid markets. We introduce the Deep Log-Sum-Exp Neural Network, an architecture that leverages Deep and Transfer learning to address RND estimation in the presence of irregular and illiquid strikes. We prove key statistical properties of the model and the consistency of the estimator. We illustrate the benefits of transfer learning to improve the estimation of the RND in severe illiquidity conditions through Monte Carlo simulations, and we test it empirically on SPX data, comparing it with popular estimation methods. Overall, our framework shows recovery of the RND in conditions of extreme illiquidity with as few as three option quotes.
In this paper we study solutions to massive Type IIA supergravity which we propose are dual to co-dimension 2 monodromy defects in 6d (1,0) CFTs realised in NS5-D6-D8 brane systems, as well as in the 5d Sp(N) fixed point theory. In the first case the defects are studied holographically as solutions to 7d $U(1)$ gauged supergravity that asymptote locally to its maximally supersymmetric $\text{AdS}_7$ vacuum away from the defects. In the second case they are dual to solutions to 6d $U(1)^2$ gauged supergravity that asymptote to its maximally supersymmetric $\text{AdS}_6$ vacuum. These solutions are then uplifted to massive Type IIA supergravity using known consistent truncations previously constructed in the literature. We compute the defect entanglement entropy and provide evidence that for the 3d defects, the entanglement entropy can be written as a linear combination of the free energy and conformal weight of the defect. Finally, we construct new co-dimension 2 monodromy defects in 6d and 5d CFTs compactified on Riemann surfaces and/or spindles.
We compute the defect entanglement entropy for co-dimension two superconformal monodromy defects in well known maximally symmetric holographic theories of various dimension. In each case we explicitly relate the universal part of the defect entanglement entropy to field theory data characterising the defect conformal field theory. We provide evidence that, unlike in the bulk theories in which the defects reside, the universal part of the defect entanglement entropy does not necessarily decrease along a renormalisation group flow.
An algebraic extension of the rational numbers is said to have the $\textit{Bogomolov property}$ (B) if the absolute logarithmic Weil height of its non-torsion elements is uniformly bounded from below. Given a continuous representation $ρ$ of the absolute Galois group $G_{\mathbb{K}}$ of a number field ${\mathbb{K}}$, one says that $ρ$ has (B) if the subfield of $\overline{\mathbb{Q}}$ fixed by $\mathrm{ker}\,ρ$ has (B). We prove that, if $ρ:G_{\mathbb{K}} \to \mathrm{GL}_d({\mathbb{Z}}_p)$ maps an inertia subgroup at a prime above $p$ surjectively onto an open subgroup of $\mathrm{GL}_d({\mathbb{Z}}_p)$, then $ρ$ has (B). More generally, we show that if the image of inertia is open in the image of the decomposition group, the normal closure of the local image is sufficiently large in the global one, and a certain condition on the center of $ρ(G_{\mathbb{K}})$ satisfied, then $ρ$ has (B). In particular, no assumption on the modularity of $ρ$ is needed, contrary to previous work of Habegger and Amoroso--Terracini. We provide several examples both in modular and non-modular cases. Our methods rely on a result of Sen comparing the ramification and Lie filtrations on the $p$-adic Lie group $ρ(G_{\mathbb{K}})$.
We perform a complete classification of AdS$_2$ solutions of Type II supergravity realising $\mathcal{N}=6$ supersymmetry and OSp$(6|2)$ superconformal symmetry on backgrounds that are foliations of AdS$_2 \times \mathbb{CP}^3$ over a Riemann surface $Σ_2$. Such solutions only exist in type IIB supergravity and are in 1 to 1 correspondence with a fourth order PDE that can be locally solved in terms of two holomorphic functions. Particular solutions in the class are the T-duals of the $\text{AdS}_3\times \mathbb{CP}^3$ and $\text{AdS}_2\times \text{S}^7$ solutions to massive Type IIA supergravity found in the literature. We discuss the field theory interpretation of the two sub-classes of solutions related to $\text{AdS}_3\times \mathbb{CP}^3$ by Abelian and non-Abelian T-duality, which provide explicit examples for the Riemann surface an annulus or a strip. In the second case we interpret the solutions as holographic duals to baryon vertex configurations realised in D2-brane box models.
This paper presents a novel general-purpose guided stereo paradigm that mimics the active stereo principle by replacing the unreliable physical pattern projector with a depth sensor. It works by projecting virtual patterns consistent with the scene geometry onto the left and right images acquired by a conventional stereo camera, using the sparse hints obtained from a depth sensor, to facilitate the visual correspondence. Purposely, any depth sensing device can be seamlessly plugged into our framework, enabling the deployment of a virtual active stereo setup in any possible environment and overcoming the severe limitations of physical pattern projection, such as the limited working range and environmental conditions. Exhaustive experiments on indoor and outdoor datasets featuring both long and close range, including those providing raw, unfiltered depth hints from off-the-shelf depth sensors, highlight the effectiveness of our approach in notably boosting the robustness and accuracy of algorithms and deep stereo without any code modification and even without re-training. Additionally, we assess the performance of our strategy on active stereo evaluation datasets with conventional pattern projection. Indeed, in all these scenarios, our virtual pattern projection paradigm achieves state-of-the-art performance. The source code is available at: https://github.com/bartn8/vppstereo.
We derive necessary and sufficient conditions for AdS$_3$ solutions of $d=11$ supergravity to preserve ${\cal N}=(1,1)$ supersymmetry in terms of G-structures. Such solutions necessarily support an SU(3)-structure on the internal 8-manifold M$_8$, in terms of which we phrase the conditions for supersymmetry preservation. We use this to derive the local form of all ${\cal N}=(4,4)$ supersymmetric AdS$_3$ solutions in $d=11$, for which M$_8$ decomposes as a foliation of a 3-sphere over a 5 dimensional base. There are 3 independent classes, 2 of which preserve the small superconformal algebra and one preserving its large counterpart for which M$_5$ contains a second 3-sphere. We show that for each solution with large (4,4) supersymmetry there are two corresponding solutions with small $(4,4)$, one for which M$_5$ maintains its 3-sphere, one where this blows up to $\mathbb{R}^3$ which can be compactified to $\mathbb{T}^3$. We use our results to construct several new solutions that lie within our derived classes as well as recovering some existing solutions.