Nilpotence and K-theory

The Nilpotence Conjecture in K-theory of Toric Varieties

It is shown that all nontrivial elements in higher K-groups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine toric varieties. 1. Statement of the main result The nilpotence conjecture in K-theory of toric varieties, treated in our previous works, asser...

Nilpotence in Stable Homotopy Theory

This talk covers most of section 4 in the Mathew-Naumann-Noel paper [MNN15]. We first discuss nilpotence in an arbitrary symmetric monoidal stable ∞-category. We then discuss the historical origins of nilpotence in the stable homotopy category, namely the Ravenel conjectures and the Nilpotence theorem proved by Devinatz-Hopkins-Smith.

Nilpotence and Periodicity in Stable Homotopy Theory

Contents Preface xi Introduction xiii 1 The main theorems 1 1.

Nilpotence and Stable Homotopy Theory II

Construction Methods for Sign Patterns Allowing Nilpotence of Index k

In this paper, the smallest such integer k is called by the index (of nilpotence) of B such that B = 0. In this paper, we study sign patterns allowing nilpotence of index k and obtain four methods to construct sign patterns allowing nilpotence of index at most k, which generalizes some recent results.