Related papers: The relative Hodge-Tate spectral sequence -- an ov…
We analyze the functorial and multiplicative properties of the Thom spectrum functor in the setting of symmetric spectra, and we establish the relevant homotopy invariance.
Let $K$ be a complete discrete valuation field of characteristic $0$ with not necessarily perfect residue field of characteristic $p>0$. We define a Faltings extension of $\mathcal{O}_K$ over $\mathbb{Z}_p$, and we construct a Hodge-Tate…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
In this paper, we introduce the concept of relative convex sequences and establish their fundamental properties, highlighting their similarities to those of convex sequences. Additionally, we prove new inequalities of the Lupas and…
Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the…
We discuss convergence in the Fourier algebra A(G) of a locally compact group G and provide a new characterisation of the local spectral sets of G.
We construct splittings of some completions of the Z/(p)-Tate cohomology of E(n) and some related spectra. In particular, we split (a completion of) tE(n) as a (completion of) a wedge of E(n-1)'s as a spectrum, where t is shorthand for the…
One of the most important invariants in singularity theory is the Hodge spectrum. Calculating the Hodge spectrum is a difficult task and formulas exist for only a few cases. In this article the main result is the formula for reduced…
We define a relative version of the Loday construction for a sequence of commutative S-algebras $A \rightarrow B \rightarrow C$ and a pointed simplicial subset $Y \subset X$. We use this to construct several spectral sequences for the…
We prove compatibility relations between mixed Hodge numbers of $k$-Du Bois fibers in flat projective families and versal deformations of isolated $k$-Du Bois singularities. These extend the notion of polarized relations in asymptotic Hodge…
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 show that a large number of Thom spectra, i.e. colimits of morphisms $BG\to BGL_1(\mathbb{S})$, can be obtained as iterated Thom spectra, i.e. colimits of morphisms $BG\to BGL_1(Mf)$ for some Thom spectrum $Mf$. This leads to a number of…
We survey recent developments in the study of Hodge theoretic aspects of Alexander-type invariants associated with smooth complex algebraic varieties.
The spectral and localization properties of $\mathcal{PT}$-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are…
In previous work with Niles Johnson the author constructed a spectral sequence for computing homotopy groups of spaces of maps between structured objects such as G-spaces and E_n-ring spectra. In this paper we study special cases of this…
In homotopy theory, exact sequences and spectral sequences consist of groups and pointed sets, linked by actions. We prove that the theory of such exact and spectral sequences can be established in a categorical setting which is based on…
The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its…
Hodge Laplacians have been previously proposed as a natural tool for understanding higher-order interactions in networks and directed graphs. Here we introduce a Hodge-theoretic approach to spectral theory and dimensionality reduction for…
We study the de Rham cohomology and the Hodge to de Rham spectral sequence for supervarieties.
We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like…