Related papers: The weight and rank filtrations

In the first half of this article we define a new weight homology functor on Voevodsky's category of effective motives, and investigate some of its properties. In special cases we recover Gillet-Soul\'e's weight homology, and Geisser's…

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for GL_n(Z).

In this note we prove some results in flat and differential $K$-theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the…

For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, we prove the existence of a canonical…

In a preprint released in 2016, Daniel Grayson introduces a conjectural presentation of the (higher) relative algebraic $K$-groups using purely combinatorial means. In this paper, we will show that this presentation is isomorphic to the…

Let k be an algebraically closed subfield of the complex numbers, and X a variety defined over k. One version of the Beilinson-Hodge conjecture that seems to survive scrutiny is the statement that the Betti cycle class map cl_{r,m} :…

We present multiresidue formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 U_q(\hat sl_2) quantum Knizhnik--Zamolodchikov equation at generic values of the quantum parameter q. These allow for…

We give a concise introduction to the Farrell-Jones Conjecture in algebraic $K$-theory and to some of its applications. We survey the current status of the conjecture, and we illustrate the two main tools that are used to attack it:…

The purpose of this paper is to show how a congruence between (the Fourier coefficients of) a Hilbert cusp form and a Hilbert Eisenstein series of parallel weight $2$ gives rise to congruences between algebraic parts of critical values of…

We develop a version of controlled algebra for simplicial rings. This generalizes the methods which lead to successful proofs of the algebraic K- theory isomorphism conjecture (Farrell-Jones Conjecture) for a large class of groups. This is…

In this article, we show that a conjecture raised in [KLMR], which regards the coefficient of the highest term when we evaluate the sl_2 weight system on the projection of a diagram to primitive elements, is a consequence of the…

We present a proof of a recent conjecture due to M. Kazarian, E. Krasilnikov, S. Lando, and M. Shapiro, which describes the average value of the universal $\mathfrak{gl}$-weight system on permutations. The proof uses a quantum analogue of…

We show that functorial equivalences can offer new insight into the blockwise Galois Alperin weight conjecture (BGAWC). Inspired by Kn\"orr and Robinson's work, we first formulate the BGAWC in terms of alternating sums indexed by chains of…

The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…

Let A be a simple, unital, exact, and finite C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup obtained from the Elliott invariant…

This is a survey on the topic explained in the title, for the proceedings on the K-theory 1997 summer institute in Seattle.

The additivity theorem for derivateurs associated to complicial biWaldhausen categories is proved. Also, to any exact category in the sense of Quillen a K-theory space is associated. This K-theory is shown to satisfy the additivity,…

$K^2 S^2 T [5]$ recently derived a new 6$^{th}$-order wave equation $KdV6$: $(\partial^2_x + 8u_x \partial_x + 4u_{xx})(u_t + u_{xxx} + 6u_x^2) = 0$, found a linear problem and an auto-B${\ddot{\rm{a}}}$ckclund transformation for it, and…

Inspired by the quantitative $K$-theory, in this paper, we introduce the coarse Baum-Connes conjecture with filtered coefficients which generalizes the original conjecture. There are two advantages for the conjecture with filtered…