Related papers: The weight and rank filtrations
The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…
The purpose of this article is to show a version of d\'evissage theorem of non-connective $K$-theory. Our theorem contains Quillen's d\'evissage theorem, Waldhausen's cell filtration theorem and theorem of heart as special cases. In this…
In this paper we formulate and lay the foundations for the K-theoretic Farrell-Jones Conjecture for the Hecke algebra of totally disconnected groups. The main result of his paper is the proof that it passes to closed subgroups. Moreover, we…
We discuss the relationship between different notions of "integrality" in motivic cohomology/K-theory which arise in the Beilinson and Bloch-Kato conjectures, and prove their equivalence in some cases for products of curves (used in the…
We study ranked enumeration for Conjunctive Queries (CQs) where the answers are ordered by a given ranking function (e.g., an ORDER BY clause in SQL). We develop "any-k" algorithms, which, without knowing the number k of desired answers,…
In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka…
We prove some $K$-theoretic descent results for finite group actions on stable $\infty$-categories, including the $p$-group case of the Galois descent conjecture of Ausoni-Rognes. We also prove vanishing results in accordance with…
We review various K-theory classification conjectures in string theory. Sen conjecture based proposals classify D-brane trajectories in backgrounds with no H flux, while Freed-Witten anomaly based proposals classify conserved RR charges and…
We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain…
We show that Pashin's conjecture on the vanishing of rational higher K-groups of smooth, projective varieties over finite fields can be thought of as a combination of three weaker conjectures.
The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed…
We show that separable, simple, unital C*-algebras with finite decomposition rank absorb the Jiang-Su algebra Z tensorially. This has a number of consequences for Elliott's program to classify nuclear C*-algebras by their K-theory data. In…
Similar to topological spaces, we introduce the Cantor-Bendixson rank of a tree $T$ by repeatedly removing the leaves and the isolated vertices of $T$ using transfinite recursion. Then, we give a representation of a tree $T$ as a leafless…
We find lower bounds on the rank of a "real" vector bundle over an involutive space, such that "real" vector bundles of higher rank have a trivial summand and such that a stable isomorphism for such bundles implies ordinary isomorphism. We…
We study weight multiplicities in tensor powers of the adjoint representation of $SU(3)$ and relate them to Franel numbers.
Pulling back the weight systems associated with the exceptional Lie algebras and their standard representations by a modification of the universal Vassiliev-Kontsevich invariant yields link invariants; extending them to coloured 3-nets, we…
We determine the quantum filtration structure of the Lee homology of all torus links. In particular, this determines the $s$-invariant of a torus link equipped with any orientation. In the special case $T(n,n)$, our result confirms a…
The log-rank conjecture is a longstanding open problem with multiple equivalent formulations in complexity theory and mathematics. In its linear-algebraic form, it asserts that the rank and partitioning number of a Boolean matrix are…
We introduce the new concept of weighted $K$-$k$-Schur functions -- a novel family within the broader class of Katalan functions -- that unifies and extends both $K$-$k$-Schur functions and closed $k$-Schur Katalan functions. This new…
We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several examples which we…