Dimensional homotopy t-structures in motivic homotopy theory

Galois Equivariance and Stable Motivic Homotopy Theory

For a finite Galois extension of fields L/k with Galois group G, we study a functor from the G-equivariant stable homotopy category to the stable motivic homotopy category over k induced by the classical Galois correspondence. We show that after completing at a prime and η (the motivic Hopf map) this results in a full and faithful embedding whenever k is real closed and L = k[i]. It is a full a...

Motivic Homotopy Theory of Group Scheme Actions

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 homotopical purity and blow-up theorems for finite abelian groups.

Topology Seminar Non-nilpotent elements in motivic homotopy theory

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∗...

Open Problems in the Motivic Stable Homotopy Theory, I

Homotopy Theory of Homotopy Algebras

The goal of this paper is to study the homotopy theory of homotopy algebras over a Koszul operad with their infinity morphisms. The method consists in endowing the category of coalgebras over the Koszul dual cooperad with a model category structure. CONTENTS Introduction 1 1. Recollections 2 2. Model category structure for coalgebras 5 3. Conclusion 14 Appendix A. A technical lemma 15 Reference...