Related papers: Algebraic Cycles of a Fixed Degree

The purpose of this paper is to describe a method for computing homotopy groups of the space of $\alpha$-stable representations of a quiver with fixed dimension vector and stability parameter $\alpha$. The main result is that the homotopy…

In the integral cohomology ring of the classifying space of the projective linear group $PGL_n$ (over $\mathbb{C}$), we find a collection of $p$-torsions $y_{p,k}$ of degree $2(p^{k+1}+1)$ for any odd prime divisor $p$ of $n$, and $k\geq…

We study the stable motivic homotopy groups $\pi_{s,w}$ of the 2-completion of the motivic sphere spectrum over $\mathbb{C}$. When arranged in the $(s,w)$-plane, these groups break into four different regions: a vanishing region, an…

A C*-algebra is said to be K-stable if its nonstable K-groups are naturally isomorphic to the usual K-theory groups. We study continuous $C(X)$-algebras, each of whose fibers are K-stable. We show that such an algebra is itself K-stable…

Let $\bar{X}$ be a smooth quasi-projective $d$-dimensional variety over a field $k$ and let $D$ be an effective Cartier divisor on it. In this note, we construct cycle class maps from (a variant of) the higher Chow group with modulus of the…

In this article we determine the stable cohomology groups H^i_s (A_n, Z/p) of the alternating groups A_n for all integers n and i, and all primes p.

We extend the results of arXiv:2206.08295v2 by showing that any homothety in $\mathbb T^2$ is homotopic to a non-uniformly hyperbolic ergodic area preserving map, provided that its degree is at least $5^2$. We also address other small…

The positive cohomology groups of a finite group acting on a ring vanish when the ring has a norm-one element. In this note we give explicit homotopies on the level of cochains when the group is cyclic, which allows us to express any…

Fix a prime $p$ and a chromatic height $h$. We prove that the homotopy $(k,1)$-category of $L_h$-local spectra $\mathrm{h}_k\big(\mathrm{Sp}_{p,h}\big)$ is algebraic as a symmetric monoidal category when $p > O(h^2+kh)$. To achieve this, we…

Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be homotopically equivalent to $\mathbb{CP}^\infty$. In particular,…

We will present proofs for two conjectures stated in arXiv:1808.08073. The first one is that for an arbitrary manifold $W$, the homotopy classes of proper maps $W\times\mathbb{R}^n\to\mathbb{R}^{k+n}$ stabilise as $n\to\infty$, and the…

Let $p$ be a prime and let $\pi^n(X;\mathbb{Z}/p^r)=[X,M_n(\mathbb{Z}/p^r)]$ be the set of homotopy classes of based maps from CW-complexes $X$ into the mod $p^r$ Moore spaces $M_n(\mathbb{Z}/p^r)$ of degree $n$, where $\mathbb{Z}/p^r$…

We study the $RO(G)$-graded Bredon cohomology of a point in the case where $G$ is a cyclic group of odd order, expanding on the information provided by previous studies. Our methods center on the purely algebraic aspects of this matter,…

Let $(C,\underline{w})$ be a polarized nodal reducible curve. In this paper we consider coherent systems of type $(r,d,k)$ on $C$ with $k < r$. We prove that the moduli spaces of $(\underline{w},\alpha)$-stable coherent systems stabilize…

We give an explicit description of the homomorphism group H_n(p) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups H_i(q) are trivial for i at least 2 but less than n. The…

This paper is a continuation of the version I of the same title, which intends to clarify and expand the results in the last chapter of `the green book' by the second author. In particular, we give the stable homotopy groups of $p$-local…

To a "stable homotopy theory" (a presentable, symmetric monoidal stable $\infty$-category), we naturally associate a category of finite \'etale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call…

P\'osa's theorem states that any graph $G$ whose degree sequence $d_1 \le \ldots \le d_n$ satisfies $d_i \ge i+1$ for all $i < n/2$ has a Hamilton cycle. This degree condition is best possible. We show that a similar result holds for…

We prove a moving lemma for the additive and ordinary higher Chow groups of relative $0$-cycles of regular semi-local $k$-schemes essentially of finite type over an infinite perfect field. From this, we show that the cycle classes can be…

We show nilpotency and completeness results for the homotopy automorphisms of a marked n-stage for an unstable coalgebra. These objects figure in the moduli problem of unstable coalgebras. Our theorems extend classical work of Dror,…