Let $G$ be a finite group, and let $\{B_{\mathbb{C}}G\}$ the class of its classifying stack $B_{\mathbb{C}}G$ in Ekedahl's Grothendieck ring algebraic $\mathbb{C}$-stacks $K_0(\operatorname{Stacks}_{\mathbb{C}})$. We show that if has mixed Tate property, invariants $H^i(\{B_{\mathbb{C}}G\})$ defined by T. Ekedahl are zero for all $i\neq 0$. also extend construction these to fields positive char...

In this work, we study the behavior of nonabelian five-dimensional Chern-Simons term at finite temperature regime in order to verify possible nonanalyticity. We employ two methods, a perturbative and non-perturbative one. No scheme regularization is needed, nonanalyticity self-energy photon origin momentum space by conditions that do not commute, namely, static limit $(k_0=0,\vec k\rightarrow 0...

We prove that the quasi-periodic Schrödinger operator with a finitely differentiable potential has purely absolutely continuous spectrum for all phases if frequency is Diophantine and sufficiently small in corresponding $$C^k$$ topology. This extends work of Eliasson [19] Avila–Jitomirskaya [5] from analytic topology to one which much broader, revealing interesting phenomenon oscillation leads ...

This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a.~ topological groups). We determine that any in compact-open topology on self-homeomorphisms Cantor set must be uniformly discrete, a precise sense we introduce here. Uniformly discrete are particular countable, finite, residually finite and topology. The resulting form subclass am...

We establish the satisfiability threshold for random $k$-SAT all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_{\rm sat}(k)$ such that formula of clause $\alpha$ is high probability satisfiable $\alpha\lt \alpha_{\rm sat}$, and unsatisfiable $\alpha>\alpha_{\rm sat}$. show given explicitly by one-step replica symmetry breaking prediction from stat...

Abstract For a not-necessarily commutative ring $R$ we define an abelian group $W(R;M)$ of Witt vectors with coefficients in -bimodule $M$ . These groups generalize the usual big rings and prove that they have analogous formal properties structure. One main result is $W(R) := W(R;R)$ Morita invariant -linear endomorphism $f$ finitely generated projective -module characteristic element $\chi _f ...