Related papers: Introduction to Framed Correspondences
A general theory of frames of reference proposed in a preceding publication is considered here in the framework of the post-Newtonian approximation, assuming that the frame of reference is centered on a time-like geodesic. The problem of…
A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra $SH$ is recovered from modules over a commutative…
For any base field and integer $l$ invertible in $k$, we prove that $\Omega^\infty_{\mathbb{G}_m}$ and $\Omega^\infty_{\mathbb{P}^1}$ commute with hyper \'etale sheafification $L_{\acute{e}t}$ and Betti realization through infinite loop…
Covering spaces are a fundamental tool in algebraic topology because of the close relationship they bear with the fundamental groups of spaces. Indeed, they are in correspondence with the subgroups of the fundamental group: this is known as…
The category of framed correspondences $Fr_*(k)$, framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [12]. Based on the theory, framed motives are introduced and studied in [7]. The main aim of this…
Thye theory of frames for a Hilbert space plays a fundamental role in signal processing, image processing, data compression, sampling theory and much more, as well as being a fruitful area of research in abstract mathematics. In this…
The article is to construct a graded ring isomorphism between $H_0(ZF(\Delta^{\bullet}_k,\mathbb{G}_m^{\wedge *}))$ and the Milnor-Witt K-theory ring $K^{MW}_{*\geqslant 0}(k)$, where $k$ is a field of characteristic zero and $ZF_*(k)$ is…
We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of finite equivalences. Furthermore, for shifts of finite type, a…
We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We obtain the rationality of the moduli spaces.…
The aim of the present paper is to generalise Sahlqvist correspondence theory to the many-valued modal semantics defined by Fitting, assuming a perfect Heyting algebra as truth value space. We present the standard translations between…
We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…
Waldhausen's algebraic K-theory machinery is applied to motivic homotopy theory, producing an interesting motivic homotopy type. Over a field F of characteristic zero, its path components receive a surjective ring homomorphism from the…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
We abstract and generalize homotopical monadicity statements, placing in a single conceptual framework a range of old and recent recognition and characterization principles in iterated loop space theory in classical, equivariant, and…
The machinery of framed (pre)sheaves was developed by Voevodsky [V1]. Based on the theory, framed motives of algebraic varieties are introduced and studied in [GP1]. An analog of Voevodsky's Cancellation Theorem [V1] is proved in this paper…
In this thesis we compare V. Voevodsky's geometric motives to the derived category of M. Nori's abelian category of mixed motives by constructing a triangulated tensor functor between them. It will be compatible with the Betti realizations…
We define a trace map for every cohomological correspondence in the motivic stable homotopy category over a general base scheme, which takes values in the twisted bivariant groups. Local contributions to the trace map give rise to quadratic…
In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log correspondences, the dividing Nisnevich topology on log…
We propose an axiomatic characterization of coarse homology theories defined on the category of bornological coarse spaces. We construct a category of motivic coarse spectra. Our focus is the classification of coarse homology theories and…