Related papers: Effective Redshift

We state a precise conjectural isomorphism between localizations of the equivariant quantum K-theory ring of a flag variety and the equivariant K-homology ring of the affine Grassmannian, in particular relating their Schubert bases and…

We compute the MU-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n+1})$, of all $\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope…

To any pullback square of ring spectra we associate a new ring spectrum and use it to describe the failure of excision in algebraic $K$-theory. The construction of this new ring spectrum is categorical and hence allows to determine the…

This paper begins with an exposition of the author's research on the category of BP_*BP-comodules, much of which is joint with Neil Strickland. The main result of that work is that the category of E(n)_*E(n)-comodules is equivalent to a…

This paper focuses on designing a consistent and efficient filter for map-based visual-inertial localization. First, we propose a new Lie group with its algebra, based on which a novel invariant extended Kalman filter (invariant EKF) is…

For a smooth quasi-projective scheme $X$ over a field $k$ with an action of a reductive group, we establish a spectral sequence connecting the equivariant and the ordinary higher Chow groups of $X$. For $X$ smooth and projective, we show…

We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes…

Let $K$ be a closed polydisc or ball in $\C^n$, and let $Y$ be a quasi projective algebraic manifold which is Zariski locally equivalent to $\C^p$, or a complement of an algebraic subvariety of codimension $\ge 2$ in such manifold. If $r$…

It is an open question whether tight closure commutes with localization in quotients of a polynomial ring in finitely many variables over a field. Katzman showed that tight closure of ideals in these rings commutes with localization at one…

The $K$-homology ring of the affine Grassmannian of $SL_n(C)$ was studied by Lam, Schilling, and Shimozono. It is realized as a certain concrete Hopf subring of the ring of symmetric functions. On the other hand, for the quantum $K$-theory…

The Runge approximation theorem for holomorphic maps (U -> C) is a fundamental result in complex analysis. The aim of this article is to prove such a result for (pseudo-)holomorphic maps from a compact Riemann surface to a compact…

We apply quantitative (or controlled) $K$-theory to prove that a certain $L^p$ assembly map is an isomorphism for $p\in[1,\infty)$ when an action of a countable discrete group $\Gamma$ on a compact Hausdorff space $X$ has finite dynamical…

We establish a novel connection between the well-known chromatic threshold problem in extremal combinatorics and the celebrated $(p,q)$-theorem in discrete geometry. In particular, for a graph $G$ with bounded clique number and a natural…

Let $n \geq 1$, $p$ a prime, and $T(n)$ any representative of the Bousfield class of the telescope $v_n^{-1}F(n)$ of a finite type $n$ complex. Also, let $E_n$ be the Lubin-Tate spectrum, $K(E_n)$ its algebraic $K$-theory spectrum, and…

In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback-Leibler approximation of spectral densities, proposed by Pavon and…

Classical definitions of locally complete intersection (l.c.i.) homomorphisms of commutative rings are limited to maps that are essentially of finite type, or flat. The concept introduced in this paper is meaningful for homomorphisms phi :…

By using K-theory, we construct a map from the tangent space to the Hilbert scheme at a point Y to the local cohomology group. And we use this map to answer affirmatively(after slight modification) a question by Mark Green and Phillip…

We give a description of the value of a finitary localizing invariant, such as algebraic $K$-theory, on the category of sheaves on a locally coherent space $X$. This in particular includes all spaces that arise as spectra of commutative…

In this article we prove that the $KH$-asembly map, as defined by Bartels and L{\"u}ck, can be described in terms of the algebraic $KK$-theory of Cortinas and Thom. The $KK$-theory description of the $KH$-assembly map is similar to that of…

We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…