Related papers: The Local Gross-Prasad Conjecture over Archimedean…

In this paper, we prove the local converse theorem for split even special orthogonal groups over a non-Archimedean local field of characteristic zero. This is the only case left on local converse theorems of split classical groups and the…

In the first part, in the local non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We conjecture that such distributions are invariant by transposition. This would imply…

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…

The conjectural theory of local newofmrs for the split $p$-adic group ${\rm SO}_{2n+1}$, proposed by Gross, predicts that the space of local newforms in a generic representation is one-dimensional. In this note, we prove that this space is…

We prove a local-global principle for torsors under the prosolvable geometric fundamental group of an affine curve over a number field.

We prove Vojta's generalized abc conjecture for algebraic tori over function fields with exceptional sets that can be determined effectively. Additionally, we establish a version of the conjecture for toric varieties. As an application, we…

We describe the set of points of the trianguline variety over a given local Galois representation. Global analogues describing companion points in eigenvariety by [Bre14] and [HN17], can be thought of as a rational analogue to the weight…

The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint $\gamma$-factor of its $L$-parameter. In this paper, we…

We prove that the projective complex algebraic varieties admitting a large complex local system satisfy a strong version of the Green-Griffiths-Lang conjecture.

In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov…

There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove…

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as…

In this paper a proof of Conjecture 9.12 of Braverman and Kazhdan in their article "gamma-functions of representations and lifting" on the acyclicity of their l-adic gamma-sheaves over certain affine spaces is given for GL(n).

This is the last in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…

We state and prove an analogue of the Kakeya conjecture for the local field $\mathbb{F}_q(\!(t)\!)$. This extends Arsovski's result on the Kakeya conjecture to local fields of positive characteristic. We also prove the Kakeya maximal…

Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, we are able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by…

In a series of papers [Pan0], [Pan1], [Pan2], [Pan3] we give a detailed and better structured proof of the Grothendieck--Serre's conjecture for semi-local regular rings containing a finite field. The outline of the proof is the same as in…

The Grothendieck-Serre conjecture predicts that on a regular local ring, no nontrivial reductive torsor becomes trivial over the fraction field. While this conjecture has been proven in the equicharacteristic case, it remains open in the…

In this article, we will prove that the formal degree conjecture is compatible with the Deligne-Kazhdan correspondence for quasi-split groups, assuming that the local Langlands correspondence is compatible with the Deligne-Kazhdan…

We formulate a generalization of Vojta's conjecture in terms of log pairs and variants of multiplier ideals. In this generalization, a variety is allowed to have singularities. It turns out that the generalized conjecture for a log pair is…