Correspondences and stable homotopy theory by Grigory Garkusha

“…As an application, stable homotopy theory of spectra SH is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed correspondences over an algebraically closed field. …”
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Twisted stable homotopy theory by Douglas, Christopher L

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Categorical constructions in stable homotopy theory/ by 185367 Tierney, Myles

Multiplicative Structures on Algebraic K-Theory by Barwick, Clark, Barwick, Clark Edward

“…We therefore regard it as the stable homotopy theory of homotopy theories. In particular, it respects all algebraic structures, and as a result, we obtain the Deligne Conjecture for this form of $K$-theory.…”
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Dirac geometry II: coherent cohomology by Lars Hesselholt, Piotr Pstrągowski

“…We apply the general theory to stable homotopy theory and use Quillen’s theorem on complex cobordism and Milnor’s theorem on the dual Steenrod algebra to identify the Dirac stacks corresponding to $\operatorname {MU}$ and $\mathbb {F}_p$ in terms of their functors of points. …”
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The generalized Tate construction by Stroilova, Olga (Olga Y.)

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Homotopy theory of modules over diagrams of rings by J. P. C. Greenlees, B. Shipley

“…Some of this material originally appeared in the preprint “An algebraic model for rational torus-equivariant stable homotopy theory”, arXiv:1101.2511, but has been generalized here.…”
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Spectral Mackey functors and equivariant algebraic K-theory (I) by Barwick, Clark Edward

“…Finally, we employ this technology to lay the foundations of equivariant stable homotopy theory for profinite groups; the lack of such foundations has been a serious impediment to progress on the conjectures of Gunnar Carlsson. …”
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