
## 1. Motivic Homotopy Theory

1.     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 theory

#### Problem 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.)
• #### Problem 1.7.

[K. Ormsby] What can we say about the motivic Picard group?

Cite this as: AimPL: Equivariant derived algebraic geometry, available at http://aimpl.org/equideralggeom.