Related papers: Definable functoriality of tensor-triangular spect…
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group $\mathrm{SO}(3)$. The aim of this work is to make use of this tool also…
We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of this theory. In particular, we demonstrate that it exhibits…
We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with…
We discuss gluing of objects and gluing of morphisms in tensor triangulated categories. We illustrate the results by producing, among other things, a Mayer-Vietoris exact sequence involving Picard groups.
Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R^n, Hilbert spaces admit various useful…
We determine the homological residue fields, in the sense of tensor-triangular geometry, in a series of concrete examples ranging from topological stable homotopy theory to modular representation theory of finite groups.
The spectrum of a tensor-triangulated category carries a compact Hausdorff topology, called the constructible topology, also known as the patch topology. We prove that patch-dense subsets detect tt-ideals and we prove that any infinite…
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all…
For a tensor triangulated category and any regular cardinal $\alpha$ we study the frame of $\alpha$-localizing tensor ideals and its associated space of points. For a well-generated category and its frame of localizing tensor ideals we…
We study the integral torsion of the values of strict polynomial functors defined over the integers. We interpret some classical homological invariants as values of strict polynomial functors and therefore obtain estimates of the integral…
Functional determinants on various domains of the sphere and flat space are presented for scalar and spinor fields.
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…
We prove a motivic version of Landweber's exact functor theorem from topology. The main result is that the assignment given by a Landweber-type formula using the MGL-homology of a motivic spectrum defines a homology theory on the stable…
We prove the existence of various adelic-style models for rigidly small-generated tensor-triangulated categories whose Balmer spectrum is a one-dimensional Noetherian topological space. This special case of our general programme of giving…
A theorem of Bondal and Kapranov lifts representations of cohomological functors from semiorthogonal decompositions of triangulated categories. We present a version of this result for triangulated functors. To this end, we introduce…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…
The category of rational G-equivariant cohomology theories for a compact Lie group $G$ is the homotopy category of rational G-spectra and therefore tensor-triangulated. We show that its Balmer spectrum is the set of conjugacy classes of…