相关论文: Survey on bounding Selmer groups for Rankin--Selbe…

We study the Beilinson-Bloch-Kato conjecture for polarized motives. In the conjugate self-dual case, we show that if the central $L$-value does not vanish, then the associated Bloch-Kato Selmer group with coefficients in a suitable local…

In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that…

We show that the Euler system associated to Rankin--Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular forms vary in $p$-adic Coleman families. We prove an explicit…

We formulate the local Langlands conjecture for connected reductive groups over local fields, including the internal parametrization of L-packets using endoscopy.

We prove a special case of the Bloch-Kato conjecture for adjoint motives associated to modular abelian surfaces.

Our first goal in this note is to explain that a weak form of Perrin-Riou's conjecture on the non-triviality of Beilinson-Kato classes follows as an easy consequence of the Iwasawa main conjectures, and deduce its refined versions in the…

We formulate the normalized period conjecture proposed by Ben-Zvi, Sakellaridis and Venkatesh in the framework of the categorical local Langlands correspondence and study its relation to distinction problems. Motivated by the work of Feng…

We establish the local Langlands conjecture for small rank general spin groups $GSpin_4$ and $GSpin_6$ as well as their inner forms. We construct appropriate $L$-packets and prove that these $L$-packets satisfy the properties expected of…

In this paper we give a proof of the Bloch-Kato conjecture relating motivic cohomology and etale cohomology. It is a corrected version of the paper with the same title which posted earlier.

We formulate some refinements and complements to the categorical local Langlands conjecture of Fargues-Scholze. In particular, we state the expected compatibilities with Eisenstein series and duality, and explain some of their consequences.…

This article has three goals. First, we generalize the result of Deuring and Serre on the characterization of supersingular locus of modular curves to all Shimura varieties given by totally indefinite quaternion algebras over totally real…

This note explains an approach to producing examples of 'generalized Kuga-Satake theory' based on establishing special cases of Simpson's conjecture that rigid local systems are motivic. This strategy is then carried out, using work of…

We make explicit Serre's generalization of the Sato-Tate conjecture for motives, by expressing the construction in terms of fiber functors from the motivic category of absolute Hodge cycles into a suitable category of Hodge structures of…

Beginning with the conjecture of Artin and Tate in 1966, there has been a series of successively more general conjectures expressing the special values of the zeta function of an algebraic variety over a finite field in terms of other…

We propose a refined version of the Beilinson-Bloch conjecture for the motive associated with a modular form of even weight. This conjecture relates the dimension of the image of the relevant p-adic Abel-Jacobi map to certain combinations…

In one of our previous articles, we outlined the formulation of a version of the categorical arithmetic local Langlands conjecture. The aims of this article are threefold. First, we provide a detailed account of one component of this…

We study conjectures of Ben-Zvi--Sakellaridis--Venkatesh that categorify the relationship between automorphic periods and $L$-functions in the context of the Geometric Langlands equivalence. We provide evidence for these conjectures in some…

Relative Langlands duality structures the study of automorphic periods around a putative duality between certain group actions of Langlands dual reductive groups. In this article, after giving a self-contained exposition of the relevant…

The Beilinson--Bloch conjecture is a generalization of the Birch and Swinnerton-Dyer conjecture, which relates the ranks of Chow groups of smooth projective varieties over global fields to the order of vanishing of $L$-functions. We prove…

Using the ring space of sheared Witt vectors, we define certain ring stacks. We suggest several models for the ring stacks. Motivation: there is a conjectural description of the stack of n-truncated Barsotti-Tate groups and its Shimurian…