Related papers: Arithmetic monodromy of hyper-K\"ahler varieties o…
We consider algebraic varieties canonically associated to any Lie superalgebra, and study them in detail for super-Poincar\'e algebras of physical interest. They are the locus of nilpotent elements in (the projectivized parity reversal of)…
We prove a Hodge-type decomposition for the de-Rham cohomology of $ p$-adically uniformized varieties by the product of Drinfeld's symmetric spaces. It is based on work of Schneider, Stuhler, Iovita and Spiess on the cohomology of…
We prove that the relative p-adic monodromy theorem holds over a dense open subset. Moreover, we establish the equivalence of the following two statements: the local constancy of the Newton polygon function associated with a de Rham local…
We show that the Euler system for the Asai representation corresponding to a Hilbert modular eigenform over a real quadratic field, constructed by Lei, Loeffler and Zerbes (2018), can be interpolated $p$-adically as the Hilbert modular form…
In this paper we define the notion of a hyperk\"ahler manifold (potentially) of Jacobian type. If we view hyperk\"ahler manifolds as "abelian varieties", then those of Jacobian type should be viewed as "Jacobian varieties". Under a minor…
We study certain complexes of differential forms, including reverse de Rham complexes, on (real or complex) Poisson manifolds, especially holomorphic log-symplectic ones. We relate these to the degeneracy divisor and rank loci of the…
Uniform $L^\infty$ and H\"older estimates were proved by the Kolodziej for complex Monge-Amp\`ere equations on compact K\"ahler manifolds with $L^p$ volume measure with $p>1$. On the other hand, establishing H\"older estimates on singular…
On a compact K\"ahler manifold there is a canonical action of a Lie-superalgebra on the space of differential forms. It is generated by the differentials, the Lefschetz operator and the adjoints of these operators. We determine the…
In this paper we solve several problems concerning joint similarity to n-tuples of operators in noncommutative varieties in $[B(\cH)^n]_1$ associated with positive regular free holomorphic functions in $n$ noncommuting variables and with…
We define cohomological complexes of locally compact abelian groups associated with varieties over $p$-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact…
We relate the dimensions of $L^p$ reduced cohomology spaces in degree k of an ALE manifold to the dimension of some spaces of decaying harmonic forms, depending both on p and on k. In this class of manifolds, this provides an extension to…
The goal of this paper is to illustrate different approaches to understand Euler characteristics in the setting of totally real commutative and non-commutative Iwasawa theory. In addition to this, and in the spirit of Hesselholt and…
We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the…
In this paper, we generalize all the results obtained on para-K\"ahler Lie algebras in Journal of Algebra {\bf 436} (2015) 61-101 to para-K\"ahler Lie algebroids. In particular, we study exact para-K\"ahler Lie algebroids as a…
We study the Picard-Lefschetz formula for the Siegel modular threefold of paramodular level and prove the weight-monodromy conjecture for its middle degree inner cohomology with arbitrary automorphic coefficients. We give some applications…
The abelian category of tetramodules over an associative bialgebra $A$ is related with the Gerstenhaber-Schack (GS) cohomology as $Ext_\Tetra(A,A)=H_\GS(A)$. We construct a 2-fold monoidal structure on the category of tetramodules of a…
We strengthen the compatibility between local and global Langlands correspondences for GL_{n} when n is even and l=p. Let L be a CM field and \Pi\ a cuspidal automorphic representation of GL_{n}(\mathbb{A}_{L}) which is conjugate self-dual…
In this paper, we establish a logarithmic vanishing theorem on weakly pseudoconvex K\"ahler manifolds, where the divisor may have infinitely many irreducible components. This result serves as a generalization of Norimatsu's findings on…
In this paper, we first construct the controlling algebras of embedding tensors and Lie-Leibniz triples, which turn out to be a graded Lie algebra and an $L_\infty$-algebra respectively. Then we introduce representations and cohomologies of…
In this article, we describe an efficient method for computing Teitelbaum's $p$-adic $\mathcal{L}$-invariant. These invariants are realized as the eigenvalues of the $\mathcal{L}$-operator acting on a space of harmonic cocycles on the…