Related papers: Nilpotent orbit theorem in $p$-adic Hodge theory

Let G be a reductive p-adic group, H(G) its Hecke algebra and S(G) its Schwartz algebra. We will show that these algebras have the same periodic cyclic homology. This might be used to provide an alternative proof of the Baum-Connes…

Let $\mathfrak{m}$ be a nilpotent ideal in the Borel subalgebra $\mathfrak{b}$ of a complex finite-dimensional semisimple Lie algebra, and $\mathfrak{m}^{\bullet}$ the subset of (ad-)nilpotent elements in $\mathfrak{b}$ such that…

We give a new construction of $p$-adic overconvergent Hilbert modular forms by using Scholze's perfectoid Shimura varieties at infinite level and the Hodge--Tate period map. The definition is analytic, closely resembling that of complex…

Let $\mathfrak{g}$ be the $p$-dimensional Witt algebra over an algebraically closed field $k$ of characteristic $p>3$. Let $\mathscr{N}={x\in\ggg\mid x^{[p]}=0}$ be the nilpotent variety of $\mathfrak{g}$, and…

This is a review article discussing the de Rham cohomology of period domains of Hodge structures. We explain it as the de Rham cohomology of differentiable stacks as of a moduli space. We also discuss the cohomology of the partial toroidal…

We give a geometric description for the dominant characteristic of a nilpotent orbit in an arbitrary finite-dimensional rational G-module. In particular, we obtain a generalization of a recent result of Gunnells-Sommers, see…

In this paper we describe geometry of orbits of upper triangular matrices of nilpotent order 2 under conjugation by the group of upper triangular invertible matrices in terms of link patterns. Further we apply this description to the…

This paper was motivated by the following question: Recall that for a smooth projective variety X whose polarized Hodge structure on H^n(X,Q)_{prim} leads to a period point ...

Using methods of p-adic analysis we give a different proof of Burnside's problem for automorphisms of quasiprojective varieties X defined over a field of characteristic 0. More precisely, we show that any finitely generated torsion subgroup…

The first obstacle in building a Geometric Quantization theory for nilpotent orbits of a real semisimple Lie group has been the lack of an invariant polarization. In order to generalize the Fock space construction of the quantum mechanical…

We compute the p-torsion and p-adic etale cohomologies with compact support of period domains over local fields in the case of basic isocrystals for quasi-split reductive groups. For the p-torsion case, we follow the method used by Orlik in…

We prove $p$-adic versions of a classical result in arithmetic geometry stating that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a subgroup by a torsion point. We do so in the context of…

We review some recent results and conjectures saying that, roughly speaking, periodic cyclic homology of a smooth non-commutative algebraic variety should carry all the additional "motivic" structures possessed by the usual de Rham…

In the paper "The Second cohomology of nilpotent orbits in classical Lie algebras, Kyoto J. Math. 60 (2020), no. 2, 717-799" by I. Biswas, P. Chatterjee and C. Maity homotopy types of nilpotent orbits are explicitly described in the case of…

In this article, we develop a systematic cohomological framework for the study of the rigidity of nilpotent Lie foliations with respect to solvable deformations. We introduce the deformation complex associated to a pair of Lie algebras…

Given a pair of nilpotent orbits in a simple Lie algebra, one can associate a pair of vertex algebras called affine W-algebras. Under some compatibility conditions on these orbits, we prove that one of these W-algebras can be obtained as…

It is known that the semi-infinite cohomology spaces of the infinitely twisted nilpotent subalgebra in an affine Lie algebra $g$ with coefficients in an integrable simple module over the affine Lie algebra have a base enumerated by elements…

A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in…

We study the wave-front set of an element in a $p$-adic reductive Lie algebra (for $p\gg\operatorname{rank}$), namely the set of maximal nilpotent orbits appearing in its Shalika germ expansion. By adapting an algorithm of Waldspurger that…

We introduce a homothetic extension of classical Weyl integrable geometry by generalizing the usual linear gauge transformations to affine homothetic transformations centered at a distinguished harmonic, scale-invariant form $\alpha_d$.…