1. Motivic Homotopy Theory
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In [MR3406512], Blumberg and Hill define $N_{\infty}$-operads, equivariant generalizations of $E_{\infty}$-operads.
Problem 1.1.
[J. Heller] What is the motivic analogue of an $N_{\infty}$-operad or in other words, what are the analogues of $G$-commutative ring spectra in motivic homotopy theory? -
Problem 1.2.
[V. Stojanoska] Can we construct an Eilenberg-Moore spectral sequence in motivic homotopy theory? -
Problem 1.3.
[K. Wickelgren] Can we construct a Serre spectral sequence in motivic homotopy theory? -
Long Term
Problem 1.4.
[A. Blumberg] Do we have a motivic description akin to adding transfers? -
In classical homotopy theory, there are, among many others, three important notions/results:
(1) The Freudenthal suspension theorem
(2) The Barratt-Priddy-Quillen theorem
(3) Infinite loop space theoryProblem 1.5.
[K. Ormsby] Can we construct/prove the above notions in the context of motivic homotopy theory? -
Problem 1.6.
[K. Ormsby] What more can we say about the tensor triangular geometry of the motivic stable homotopy category? (See [arxiv:1608.02876] for a list of questions.)
Cite this as: AimPL: Equivariant derived algebraic geometry, available at http://aimpl.org/equideralggeom.