Related papers: On depth-zero integral models of local Shimura var…

We consider degenerations of all simple Lie algebras of exceptional type obtained by embedding into affine Lie algebras. We give a filtration to consider this as an abelianisation of the original Lie algebra. We then show that the…

We analyze the asymptotic behavior of certain twisted orbital integrals arising from the study of affine Deligne-Lusztig varieties. The main tools include the Base Change Fundamental Lemma and $q$-analogues of the Kostant partition…

In this paper we describe a machinery for homological calculations of representations of FI_G, and use it to develop a local cohomology theory over any commutative Noetherian ring. As an application, we show that the depth introduced by the…

We construct Nakajima's quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy's) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into…

Motivated by the problem of giving an explicit description of the basic locus in the reduction of Shimura varieties, G\"{o}rtz, He and Nie studied the cases where the basic affine Deligne-Lusztig variety, which serves as its group-theoretic…

We prove finiteness and base change properties for analytic cohomology of families of $L$-analytic $(\varphi_L,\Gamma_L)$-modules parametrised by affinoid algebras in the sense of Tate. For technical reasons we work over a field $K$…

The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected…

This survey article explains the construction of Rapoport-Zink local models and their use in understanding various questions relating to the singularities in the reduction modulo p of certain Shimura varieties with parahoric level structure…

We investigate a class of Leibniz algebroids which are invariant under diffeomorphisms and symmetries involving collections of closed forms. Under appropriate assumptions we arrive at a classification which in particular gives a…

We develop a new method for obtaining branching rules for affine Kac-Moody Lie algebras at negative integer levels. This method uses fusion rules for vertex operator algebras of affine type. We prove that an infinite family of ordinary…

In this paper we construct Shimura subvarieties of dimension bigger than one of the moduli space of polarised abelian varieties of a given dimension, which are generically contained in the Pym loci of (ramified) double covers. The idea is…

It is a classic result of Segerberg and Maksimova that a variety of $\mathsf{S4}$-algebras is locally finite iff it is of finite depth. Since the logic $\mathsf{MS4}$ (monadic $\mathsf{S4}$) axiomatizes the one-variable fragment of…

We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms.…

We prove a conjecture of Pappas and Rapoport for all Shimura varieties of abelian type with parahoric level structure when $p>3$ by showing that the Kisin-Pappas-Zhou integral models of Shimura varieties of abelian type are canonical. In…

Using Bruhat-Tits theory, we analyse the restriction of depth-zero representations of a semisimple simply connected $p$-adic group $G$ to a maximal compact subgroup $K$. We prove the coincidence of branching rules within classes of…

The local Langlands correspondence for GL(n) of a non-Archimedean local field $F$ parametrizes irreducible admissible representations of $GL(n,F)$ in terms of representations of the Weil-Deligne group $WD_F$ of $F$. The correspondence,…

We prove Rapoport's dimension conjecture for affine Deligne-Lusztig varieties for GL_h and superbasic b. From this case the general dimension formula for affine Deligne-Lusztig varieties for special maximal compact subgroups of split groups…

In a previous paper it was shown that a certain family of varieties suggested by Lusztig, is not enough to construct all irreducible complex representations of reductive groups over finite rings coming from the ring of integers in a local…

We show that the compactly supported cohomology of certain $\mathrm{U}(n,n)$ or $\mathrm{Sp}(2n)$-Shimura varieties with $\Gamma_1(p^\infty)$-level vanishes above the middle degree. The only assumption is that we work over a CM field $F$ in…

We study multivariate Mellin transforms of Laurent polynomials by considering special toric compactifications which make their singular structure apparent. This gives a precise description of their convergence domain, refining results of…