Related papers: On the exponential local-global principle for mero…

In this paper we will algorithmically prove the local and global epsilon constant conjectures for all fields of absolute degree lower or equal to 15. To this end we will present an efficient algorithm for the computation of local…

We introduce the theory of unipotent morphisms of algebraic stacks and prove a surprising local to global principle for a class of vector bundles. Two sample applications of our methods are the following: (1) a unipotent analogue of…

In this paper, we extend a spherical variant of the Kowalski-S\{l}odkowski theorem due to Li, Peralta, Wang and Wang. As a corollary, we prove that every 2-local map in the set of all surjective isometries (without assuming linearity) on a…

We prove the failure of the local-global principle, with respect to discrete valuations, for isotropy of quadratic forms over function fields of transcendence degree at least 2 over algebraically closed fields. Our construction involves…

Following the work of Harris and Kudla we prove a more general form of a conjecture of Jacquet relating the non-vanishing of a certain period integral to non-vanishing of the central critical value of a certain $L$-function. As a…

In this paper, we completely prove a standard conjecture on the local converse theorem for generic representations of GLn(F), where F is a non-archimedean local field.

A local existence and uniqueness theorem for ODEs in the special algebra of generalized functions is established, as well as versions including parameters and dependence on initial values in the generalized sense. Finally, a Frobenius…

In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schr\"odinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such…

We develop a wavelet like representation of functions in $L^p(\mathbb{R})$ based on their Fourier--Hermite coefficients; i.e., we describe an expansion of such functions where the local behavior of the terms characterize completely the…

In this article we study an abelian analogue of Schanuel's conjecture. This conjecture falls in the realm of the generalised period conjecture of Y. Andr{\'e}. As shown by C. Bertolin, the generalised period conjecture includes Schanuel's…

In this note we study several topics related to the schema of local reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with $\Sigma_n$-definable parameters,…

We investigate local-global principles for Galois cohomology, in the context of function fields of curves over semi-global fields. This extends work of Kato's on the case of function fields of curves over global fields.

In this paper, we prove the local converse conjecture of Jacquet over p-adic fields for GL(n) using Bessel functions.

We prove a non-minimal modularity lifting theorem for ordinary Galois representations over imaginary quadratic fields, conditional on a local-global compatibility conjecture for ordinary torsion classes.

We prove a local converse theorem for $GL_n$ over the archimedean local fields which characterizes an infinitesimal equivalence class of irreducible admissible representations of $GL_n(\mathbb{R})$ or $GL_n(\mathbb{C})$ in terms of twisted…

This paper introduces a quaternionic analogue of toric geometry by developing the theory of local $Q^n := Sp(1)^n$-actions on 4n-dimensional manifolds, modeled on the regular representation. We identify obstructions that measure the failure…

In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg…

Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

Recently, Marian-Oprea-Pandharipande established (a generalization of) Lehn's conjecture for Segre numbers associated to Hilbert schemes of points on surfaces. Extending work of Johnson, they provided a conjectural correspondence between…