Classically, the nilpotence theorem of Devinatz, Hopkins, and Smith tells us that non-nilpotent self maps on finite p-local spectra induce nonzero homomorphisms on BP -homology. Motivically, over C, this theorem fails to hold: we have a motivic analog of BP and whilst η : S1,1 → S0,0 induces zero on BP -homology, it is nonnilpotent. Recent work with Haynes Miller has led to a calculation of ηπ∗...

For p > 2, β1 ∈ π 2p2−2p−2(S) is the first positive even-dimensional element in the stable homotopy groups of spheres. A classical theorem of Nishida [Nis73] states that all elements of positive dimension in the stable homotopy groups of spheres are nilpotent. In fact, Toda [Tod68] proved β 2−p+1 1 = 0. For p = 3 he showed that β 1 = 0 while β 5 1 6= 0. In [Rav86] the second author computed the...

Fix a field F. A zero-nonzero pattern A is said to be potentially nilpotent over F if there exists a matrix with entries in F with zero-nonzero pattern A that allows nilpotence. In this paper an investigation is initiated into which zero-nonzero patterns are potentially nilpotent over F with a special emphasis on the case that F = Zp is a finite field. A necessary condition on F is observed for...

For a one-parameter degeneration of reduced compact complex analytic spaces dimension $n$, we prove the invariance frontier Hodge numbers $h^{p,q}$ (that is, with $pq(n-p)(n-q)=0$) for intersection cohomology fibers and also their desingularizations, assuming that central fiber is reduced, projective, has only rational singularities. This can be shown to equivalent structure sheaf (which known ...

Abstract We investigate the topological nilpotence degree, in sense of Henn–Lannes–Schwartz, a connected Noetherian unstable algebra R . When is mod p cohomology ring compact Lie group, Kuhn showed how this invariant controlled by centralizers elementary abelian -subgroups. By replacing -subgroups with components Lannes’ T -functor, and utilizing techniques algebras over Steenrod algebra, we ar...