Related papers: Locally analytic completed cohomology

We show how to construct, for a Lagrangian of arbitrary order, a Lepage equivalent satisfying the closure property: that the Lepage equivalent vanishes precisely when the Lagrangian is null. The construction uses a homotopy operator for the…

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$, where $G = GL(n,\C)$, and where $K$ is one of…

We extend the techniques developed by Millson and Raghunathan to prove nonvanishing results for the cohomology of compact arithmetic quotients of hyperbolic n-space with values in the local coefficient systems associated to finite…

For any Bott-Samelson resolution $q_{I}:\hat{X_{I}}\rightarrow G/B$ of the flag variety $G/B$, and any torus equivariant oriented cohomology $h_T$, we compute the restriction formula of certain basis $\eta_L$ of $h_T(\hat{X_{I}})$…

We prove that the homology groups of any connected reductive group over a field with coefficients in the Steinberg representation vanish in a range. The generalizes work of Ash-Putman-Sam on the classical split groups. We state a…

Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related…

We compute the level groups associated with mixed Shimura varieties that appear at the boundaries of compactifications of Shimura varieties and show that the boundaries of minimal compactifications of Pappas-Rapoport integral models are…

We show that an equivariantly embedded Hermitian symmetric space in a projective space, which contains neither a projective space nor a hyperquadric as a component, is characterized by their fundamental forms as a local submanifold of the…

We study the image of $\ell$-adic representations attached to subvarieties of Shimura varieties $Sh_K(G,X)$ that are not contained in a smaller Shimura subvariety and have no isotrivial components. We show that, for $\ell$ large enough…

We show by studying the symplectic geometry of the extended moduli space that the intersection cohomology of the representation space $Hom(\pi_1(\Sigma),G)/G$ for a simply connected compact Lie group $G$ is naturally embedded into the $G$…

We compute the cohomology of the right generalised projective Stiefel manifolds and use it to find bounds on the rank of the complementary bundle for certain vector bundles. Further the cohomology computations are also used to find bounds…

We generalize the local-global compatibility result in arXiv:1506.04022 to higher dimensional cases, by examining the relation between Scholze's functor and cohomology of Kottwitz-Harris-Taylor type Shimura varieties. Along the way we prove…

For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of…

We discuss the properties of complex manifolds having rational homology of $S^1 \times S^{2n-1}$ including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known vanishing properties of cohomology of…

We construct projective toroidal compactifications for integral models of Shimura varieties of Hodge type. We also construct integral models of the minimal (Satake-Baily-Borel) compactification. Our results essentially reduce the problem to…

We construct integral models and special affinoids of suitable tubular neighborhoods of local Shimura varieties at depth-zero. We show that the reductions of the special affinoids over suitable tamely ramified extensions are realized as…

A. Sikora has shown results which confirm the analogy between number fields and 3-manifolds. However, he has given proofs of his results which are very different in the arithmetic and in the topological case. In this paper, we show how to…

We study properties of the restriction of discrete series representations of $G=U(p,q)$ to $G'= U(p-1,q)$ and the corresponding symmetry breaking operators in $\operatorname{Hom}_{G'}(\pi|_{G'}, \pi')$. This leads to the introduction of…

We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…

The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…