Related papers: Tensor-triangular fields: Ruminations
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.
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.
We explicitly present homological residue fields for tensor triangulated categories as categories of comodules in a number of examples across algebra, geometry, and topology. Our results indicate that, despite their abstract nature, they…
We give a brief introduction to tensor triangulated geometry, a brief introduction to various motivic categories, and then make some observations about the conjectural structure of the tensor triangulated spectrum of the Morel-Voevodsky…
We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.
In this paper, we study geometric points in tensor triangular geometry. In doing so, we construct a counter-example to Balmer's Nerves of Steel conjecture using free constructions in higher Zariski geometry. We then go on to introduce and…
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of…
We investigate a new notion of regularity for tensor triangulated categories, called residual regularity. We show that residual regularity descends and ascends via finite separable extensions and we classify all finite groups whose derived…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
Using homological residue fields, we define supports for big objects in tensor-triangulated categories and prove a tensor-product formula.
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three dimensional domains in which the boundary normal…
We prove that the homological and Balmer spectra in tensor-triangular geometry are functorial in certain definable functors, thereby providing an alternative perspective on functoriality in tensor-triangular geometry from the viewpoint of…
Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…
In Tensor Field Theory (TFT), observables are defined through tensor field contractions that produce unitary invariants for complex-valued tensor fields. Traditionally, these observables are constructed using tensor fields of a fixed order…
We investigate composite models of gravity and explore how dynamical tensor fields can emerge within the functional renormalization group framework. We consider two prototype models: a fermionic theory and a scalar theory. In both cases, an…
We survey recent progress in the problem of recovering a tensor field from its integrals along geodesics. We also propose several open problems.
We study Tate motives with integral coefficients through the lens of tensor triangular geometry. For some base fields, including the field of algebraic numbers and the algebraic closure of a finite field, we arrive at a complete description…