Related papers: The geometric correspondence in some special cases

In this paper, we consider the problem of finding dense intrinsic correspondence between manifolds using the recently introduced functional framework. We pose the functional correspondence problem as matrix completion with manifold…

We give a short introduction, beginning with the Kerr geometry itself, to the basic results, motivation, open problems and future directions of the Kerr/CFT correspondence.

Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded $t$-structures with length heart and (4) bounded co-$t$-structures. These correspondences are shown to commute with mutations.…

We prove the Jacquet-Langlands local correspondence in non-zero characteristic, using the proof by Deligne, Kazhdan and Vign\'eras for the zero characteristic case and the theory of closed fields of Kazhdan. We also prove the orthogonality…

Revised: just some typos, reorganized a bit the article. It will be published in the VIASM Annual meeting, Hanoi. We give a detailed account of Deligne's letter to Drinfeld dated June 18, 2011, in which he shows that there are finitely many…

Contact Geometry is an odd dimensional analogue of Symplectic Geometry. This vague idea can actually be formalized in a rather precise way by means of a Symplectic-to-Contact Dictionary. The aim of this review paper is discussing the basic…

In this paper we give several methods to construct curves over finite fields with many points and illustrate this with examples of the results.

This paper investigates the synchronization problems for general high-dimensional linear networks over finite fields. By using the technique of linear transformations and invariant subspaces for linear spaces over finite fields, several…

We investigate the birational section conjecture for curves over function fields of characteristic zero and prove that the conjecture holds over finitely generated fields over Q if it holds over number fields.

On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast…

We prove a realization of the local Langlands correspondence for two-dimensional representations of a Weil group of conductor three in the cohomology of Lubin-Tate curves by a purely local geometric method.

Over a global field (number field or function field of a curve over a finite field), theorems for the Galois cohomology of algebraic groups have long been known. For $F$ the function field of a curve over the formal series field…

We consider function fields of transcendence degree at least 2 over algebraic closures of finite fields, and describe a functorial way to recover such function fields form their pro-l Galois theory.

Recently Fukasawa, Homma and Kim introduced and studied certain projective singular curves over $\mathbb {F}_q$ with many extremal properties. Here we extend their definition to more general non-rational curves.

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…

There are only a few invariants one classically associates with precompact translation surfaces, among them certain numberfields, i.e. fields which are finite extensions of the field Q of rational numbers. These fields are closely related…

S.-Y. Pan decomposes the uniform projection of the Weil representation of a finite symplectic-odd orthogonal dual pair, in terms of Deligne-Lusztig virtual characters, assuming that the order of the finite field is large enough. In this…

All kinds of global correspondences of Langlands are evaluated from the functional representation spaces of the algebraic bilinear semigroups GL2(.x.) with entries in products,right by left,of sets of archimedean increasing completions.…

Based on the formalism of rigid-analytic motives of Ayoub--Gallauer--Vezzani, we extend our previous work with Fargues from $\ell$-adic sheaves to motivic sheaves. In particular, we prove independence of $\ell$ of the $L$-parameters…

The efficacy of using complex numbers for understanding geometric questions related to polar equations and general cycloids is demonstrated.