Related papers: On the Hodge--Tate crystals over O_K

We develop a formalism to study the implications of causality on OPE coefficients in conformal field theories with large central charge and a sparse spectrum of higher spin operators. The formalism has the interpretation of a new conformal…

It is known that the semisimplicity of quantum cohomology implies the vanishing of off-diagonal Hodge numbers (Hodge--Tateness). We investigate which hyperplane sections of homogeneous varieties possess either of the two properties. We…

Inspired by the classical Bohman-Korovkin-Wulbert (BKW) operators, we initiate a study of noncommutative BKW-operators. Let $A$ be a unital $C^*$-algebra, and $S$ be a set of generators of $A$. A unital completely positive (UCP)-map $\phi:…

To determine the Hilbert space and inner product for a quantum theory defined by a non-Hermitian $\mathcal{PT}$-symmetric Hamiltonian $H$, it is necessary to construct a new time-independent observable operator called $C$. It has recently…

We consider the problem of defining an action of Hecke operators on the coherent cohomology of certain integral models of Shimura varieties. We formulate a general conjecture describing which Hecke operators should act integrally and solve…

Let F be a real quadratic field with ring of integers O and with class number 1. Let Gamma be a congruence subgroup of GL_2 (O). We describe a technique to compute the action of the Hecke operators on the cohomology H^3 (Gamma; C). For F…

We construct the crystalline comparison isomorphisms for proper smooth formal schemes over an absolutely unramified base. Such isomorphisms hold for \'etale cohomology with nontrivial coefficients, as well as in the relative setting, i.e.…

We introduce the notion of a prism, which may be regarded as a "deperfection" of the notion of a perfectoid ring. Using prisms, we attach a ringed site -- the prismatic site -- to a $p$-adic formal scheme. The resulting cohomology theory…

We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of…

We consider a reductive dual pair (G, G') in the stable range with G' the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K'_C-orbits, where K' is a maximal compact subgroup of G' and we describe the…

We prove that the $\infty$-category of surjections of animated rings is projectively generated, introduce and study the notion of animated PD-pairs - surjections of animated rings with a "derived" PD-structure. This allows us to generalize…

This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…

For a connected simply connected nilpotent Lie group $\G$ with Lie algebra $\g$ and unitary dual $\wG$ one has (a) a global quantization of operator-valued symbols defined on $\G\times\wG$, involving the representation theory of the group,…

For fully nonlinear $k$-Hessian operators on bounded strictly $(k-1)$-convex domains $\Omega$ in ${\mathbb R}^N$, a characterization of the principal eigenvalue associated to a $k$-convex and negative principal eigenfunction will be given…

In the case of complex symplectic and orthogonal groups, we find $(\mathfrak{g}, K)-$modules with the property that their $K-$structure matches the structure of regular functions on the closures of nilpotent orbits. This establishes a…

We construct commutative algebra spectra that represent the operator $K$-theory of $C^*$-algebras, which are algebras over the commutative ring spectra that represent topological $K$-theory. The spectral multiplicative structure introduces…

These notes cover the contents of three survey lectures held at the ICTP Trieste Summer school on High dimensional manifold theory 2001. They introduce techniques coming from the theory of operator algebras. We will focus on the basic…

Let $\{\frak{M} _k \} _{ k \in \mathbb{Z}} $ be a sequence of closed subspaces of Hilbert space $H$, and let $\{\Theta_k\}_{k \in \mathbb{Z}}$ be a sequence of linear operators from $H$ into $\frak{M}_k$, $k \in \mathbb{Z}$. In the…

This paper explores operators with countable, continuous, and hybrid spectra, focusing on both finite dimensional and infinite dimensional cases, particularly in non-Hermitian systems. For finite dimensional operators, a novel concept of…

We discuss the notion of a q-PD-envelope considered by Bhatt and Scholze in their recent theory of q-crystalline cohomology and explain the relation with our notion of a divided polynomial twisted algebra. Together with an interpretation of…