Related papers: On the arithmetic transfer conjecture for exotic s…

We study the p-adic analogue of the arithmetic Gan-Gross-Prasad (GGP) conjectures for unitary groups. Let $\Pi$ be a conjugate-selfdual cuspidal automorphic representation of GL_{n} x GL_{n+1} over a CM field, which is algebraic of minimal…

We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we…

We reinterpret a conjecture of Breuil on the locally analytic $\mathrm{Ext}^1$ in a functorial way using $(\varphi,\Gamma)$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or…

In this paper, we propose a modified Kudla-Rapoport conjecture for the Kr\"amer model of unitary Rapoport-Zink space at a ramified prime, which is a precise identity relating intersection numbers of special cycles to derivatives of…

Let $G$ be a connected reductive group over a non-archimedean local field $F$ of residue characteristic $p$, $P$ be a parabolic subgroup of $G$, and $R$ be a commutative ring. When $R$ is artinian, $p$ is nilpotent in $R$, and…

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…

A group theory justification of one dimensional fractional supersymmetry is proposed using an analogue of a coset space, just like the one introduced in $1D$ supersymmetry. This theory is then gauged to obtain a local fractional…

We prove a p-adic Labesse-Langlands transfer from the group of units in a definite quaternion algebra to its subgroup of norm one elements. More precisely, given an eigenvariety for the first group, we show that there exists an eigenvariety…

This paper is the third in a series that researches the Morse Theory, gradient flows, concavity and complexity on smooth compact manifolds with boundary. Employing the local analytic models from \cite{K2}, for \emph{traversally generic…

Recently, motivated by the theory of real local Arthur packets, making use of the wavefront sets of representations over non-Archimedean local fields $F$, Ciubotaru, Mason-Brown, and Okada defined the weak local Arthur packets consisting of…

The aim of this paper is to explain how to get a complex of smooth representations out of the dual vector space to a smooth representation of a p-adic Lie group, in natural characteristic. The construction does not depend on any…

We prove a conjecture of Casselman and Shahidi stating that the unique irreducible generic subquotient of a standard module is necessarily a subrepresentation for a large class of connected quasi-split reductive groups, in particular for…

Xue proved an equational refinement of the unitary Shimura curve case of the arithmetic Gan-Gross-Prasad conjecture via the Gross-Zagier formula for quaternionic Shimura curves. On the other hand, Rapoport, Smithling and Zhang posed a…

In this paper we characterize irreducible generic representations of $\SO_{2n+1}(k)$ where $k$ is a $p$-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic…

The local Gan-Gross-Prasad conjecture of unitary groups, which is now settled by the works of Plessis, Gan and Ichino, says that for a pair of generic $L$-parameters of $(U(n+1),U(n))$, there is a unique pair of representations in their…

The K-theoretic Farrell-Jones isomorphism conjecture for a group ring $R[G]$ has been proved for several groups. The toolbox for proving the Farrell-Jones conjecture for a given group depends on some geometric properties of the group as it…

We introduce a notion of elliptic fake degrees for unipotent elliptic representations of a semisimple p-adic group. We conjecture, and verify in some cases, that the relation between the formal degrees of unipotent discrete series…

We develop the analog of crystalline Dieudonn\'e theory for p-divisible groups in the arithmetic of function fields. In our theory p-divisible groups are replaced by divisible local Anderson modules, and Dieudonn\'e modules are replaced by…

We give a new, unexpected characterization of saturated fusion systems on a p-group S in terms of idempotents in the p-local double Burnside ring of S that satisfy a Frobenius reciprocity relation, and reformulate fusion-theoretic phenomena…

We prove new fundamental lemma and arithmetic fundamental lemma identities for general linear groups over quaternion division algebras. In particular, we verify the transfer conjeture and the arithmetic transfer conjecture from…