Related papers: Nilpotence theorem in stable homotopy theory
The coexponent of a finite p-group is introduced and we consider how the nilpotency class is bounded in terms of this invariant.
We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results.
On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
Seemingly different interpretations or descriptions of Einstein's model for the heat capacity of a solid can be found in textbooks and the literature. The purpose of this note is to clarify the equivalence of the different descriptions,…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
This paper is a sequel to [1] and considers definability in differential-henselian monotone fields with c-map and angular component map. We prove an Equivalence Theorem among whose consequences are a relative quantifier reduction and an NIP…
This survey contains the main results in rational homotopy, from the beginning to the most recent ones. It makes the status of the art, gives a short presentation of some areas where rational homotopy has been used, and contains a lot of…
We prove that the isomorphism type of the subrack lattice of a finite group determines the nilpotence class. We analyze the problem of estimating the orders of the group elements corresponding to the atoms of the subrack lattice. As a…
We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish…
In this note, we find a new way to prove several properties of 2-alternating capacities.
We present a detailed analysis of the orbital stability of the Pais-Uhlenbeck oscillator, using Lie-Deprit series and Hamiltonian normal form theories. In particular, we explicitly describe the reduced phase space for this Hamiltonian…
We prove that the homotopy theory of $N_\infty$ operads is equivalent to a homotopy theory of discrete operads, and we construct free and associative operadic realizations of every indexing system. This resolves a conjecture of Blumberg and…
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
In this note we present a complete proof of the fact that all the submanifolds of a one parameter family of compact symplectic submanifolds inside a compact symplectic manifold are Hamiltonian isotopic.
Algebraic $kk$-theory, introduced by Corti\~nas and Thom, is a bivariant $K$-theory defined on the category $\mathrm{Alg}$ of algebras over a commutative unital ring $\ell$. It consists of a triangulated category $kk$ endowed with a functor…
We prove a homological stability theorem for the subgroup of the mapping class group acting as the identity on some fixed portion of the first homology group of the surface. We also prove a similar theorem for the subgroup of the mapping…
We prove a quantitative variant of a disjointness theorem of nilflows from horospherical flows following a technique of Venkatesh, combined with the structural theorems for nilflows by Green, Tao and Ziegler.
We prove a $C^\infty$ version of the Nekhoroshev's estimate on the stability times of the actions in close to integrable Hamiltonian systems. The proof we give is a variant of the original Nekhoroshev's proof and it consists in first…
We give a complete and detailed proof of Harer's stability theorem for the homology of mapping class groups of surfaces, with the best stability range presently known. This theorem and its proof have seen several improvements since Harer's…
For a scheme X, denote by SH(X_et^hyp) the stabilization of the hypercompletion of its etale infty-topos, and by SH_et(X) the localization of the stable motivic homotopy category SH(X) at the (desuspensions of) etale hypercovers. For a…