Liu, Yongqiang Maxim, Laurenţiu Wang, Botong
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positiv...

Ribón, Javier
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

We are interested in the algebraic properties of groups of local biholomorphisms and their consequences. A natural question is whether the complexity of solvable groups is bounded by the dimension of the ambient space. In this spirit we show that 2 n + 1 {2n+1} is the sharpest upper bound for the derived length of solvable subgroups of the group ...

de Courcy-Ireland, Matthew Lemm, Marius
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of dimension 3 or higher, thanks to the universality of the local Weyl law. The key technical step is an estimate capturing some cancellation in a triple integral of Bessel funct...

Chen, Miaofen Nie, Sian
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

We consider the Kisin variety associated to an n-dimensional absolutely irreducible mod p Galois representation ρ¯{\bar{\rho}} of a p-adic field K together with a cocharacter μ. Kisin conjectured that the Kisin variety is connected in this case. We show that Kisin’s conjecture holds if K is totally ramified with n=3{n=3} or μ is of a very particula...

Huang, Lan-Hsuan Lee, Dan A. Sormani, Christina
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

There is an error in the proof of Theorem 1.3 of the original article. Despite the problem, it is rigorously proved in joint work of the first two authors and Perales that Theorem 1.3 is true, using recent results of Allen and Perales that extend the work of Allen, Perales, and Sormani.

Bodin, Arnaud Dèbes, Pierre König, Joachim Najib, Salah
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

We establish a version “over the ring” of the celebrated Hilbert Irreducibility Theorem. Given finitely many polynomials in k+n{k+n} variables, with coefficients in ℤ{\mathbb{Z}}, of positive degree in the last n variables, we show that if they are irreducible over ℤ{\mathbb{Z}} and satisfy a necessary “Schinzel condition”, then the first k variabl...

Fujita, Ryo Hernandez, David Oh, Se-jin Oya, Hironori
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

Let (𝔤,𝗀){\mathfrak{g},\mathsf{g})} be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with 𝗀{\mathsf{g}} being of simply-laced type. We construct a collection of ring isomorphisms between the quantum Grothendieck rings of monoidal categories 𝒞𝔤{\mathscr{C}_{\mathfrak{g}}} and 𝒞𝗀{\mathscr{C...

Shimizu, Ryoji
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

Let K be a number field and S a set of primes of K. We write KS/K{K_{S}/K} for the maximal extension of K unramified outside S and GK,S{G_{K,S}} for its Galois group. In this paper, we prove the following generalization of the Neukirch–Uchida theorem under some assumptions: “For i=1,2{i=1,2}, let Ki{K_{i}} be a number field and Si{S_{i}} a set of p...

Cass, Robert
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

For a reductive group over an algebraically closed field of characteristic p>0{p>0} we construct the abelian category of perverse 𝔽p{\mathbb{F}_{p}}-sheaves on the affine Grassmannian that are equivariant with respect to the action of the positive loop group. We show this is a symmetric monoidal category, and then we apply a Tannakian formalism to ...

Jost, Jürgen Liu, Lei Zhu, Miaomiao
Published in
Journal für die reine und angewandte Mathematik (Crelles Journal)

In this paper, we solve a new elliptic-parabolic system arising in geometric analysis that is motivated by the nonlinear supersymmetric sigma model of quantum field theory. The corresponding action functional involves two fields, a map from a Riemann surface into a Riemannian manifold and a spinor coupled to the map. The first field has to satisfy ...