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

For an open set in a compact smooth oriented Riemannian n-manifold and a positive finite Borel measure with support contained in the closure of the open set, we define an associated Krein-Feller operator on k-forms by assuming the Poincare…

We prove that the image of an elliptic operator on a smooth separable Hilbert fibre bundle on compact manifolds is closed with respect to the natural pre-Hilbert topology. We consider a tensor product of the operator, which is invariant…

Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm)}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian ${\cal H}$ are…

Inspired by Bhatt-Morrow-Scholze's work on ${\rm THH}$, we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log ${\rm THH}$ and its variants. Moreover, of independent…

Let $\Omega$ be a tiling space and let $G$ be the maximal group of rotations which fixes $\Omega$. Then the cohomology of $\Omega$ and $\Omega/G$ are both invariants which give useful geometric information about the tilings in $\Omega$. The…

We determine the A(1)-homotopy of the topological cyclic homology of the connective real K-theory spectrum ko. The answer has an associated graded that is a free F_2[v_2^4]-module of rank 52, on explicit generators in stems -1 \le * \le 30.…

Let G be an infinitesimal group scheme over a field k of positive characteristic p. We introduce the global p-nilpotent operator $\Theta_G: k[G] \to k[V(G)]$, where V(G) is the scheme which represents 1-parameter subgroups of G. This…

The simultaneous null solutions of the two complex Hermitean Dirac operators are focused on in Hermitean Clifford analysis, where the matrix Hilbert transform was presented and proved to satisfy the analogous properties of the Hilbert…

We investigate properties of the most general PT-symmetric non-Hermitian Hamiltonian of cubic order in the annihilation and creation operators as a ten parameter family. For various choices of the parameters we systematically construct an…

Assuming the Riemann hypothesis for $L$-functions attached to primitive Dirichlet characters, modular cusp forms, and their tensor products and symmetric squares, we write down explicit finite sets of Hecke operators that span the Hecke…

We study a known filtration of the second cohomology of a finite dimensional nilpotent Lie algebra $\mathfrak{g}$ with coefficients in a finite dimensional nilpotent $\mathfrak{g}$-module $M$, that is based upon a refinement of the…

Our main result is a theorem saying that a bounded operator $A$ on a Hilbert space belongs to a certain set associated with its self-commutator $[A^*,A]$, provided that $A-zI$ can be approximated by invertible operators for all complex…

We study H^*(P), the mod p cohomology of a finite p--group P, viewed as an Out(P)--module. In particular, we study the conjecture, first considered by Martino and Priddy, that, if e_S in Z/p[Out(P)] is a primitive idempotent associated to…

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…

Based on Johnson's operator formula for the equivariant Gromov-Witten theory of $\mathbb{P}^1$-orbifolds, we give a new approach to the operator formalism by Okounkov and Pandharipande regarding the $\mathbb{C}^*$-equivariant Gromov-Witten…

In this thesis we solve the coboundary equation $\delta c=d$ with bounds for cochains with values in a coherent subsheaf of some $\mathcal{O}^p_{\Omega}$, where $\Omega$ is a Stein manifold. In particular the existence of a finite set of…

We determine rational Kisin modules associated with two-dimensional, irreducible, crystalline representations of $\mathrm{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)$ of Hodge-Tate weights $0, k-1$. If the slope is larger than $\lfloor…

This work is devoted to the study of integral $p$-adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of $p$-adic Hodge theory with the \'etale…

We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of C_p. It takes values in a mixed-characteristic analogue of Dieudonne modules, which was previously defined by Fargues as a version of…

In a previous paper (arXiv:math-ph/0604055) we introduced a very simple PT-symmetric non-Hermitian Hamiltonian with real spectrum and derived a closed formula for the metric operator relating the problem to a Hermitian one. In this note we…