Rigidity in Equivariant Stable Homotopy Theory

For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all "higher order structure" of the 2-local G-equivariant stable homotopy category, such as the equivariant homotopy types of function G-spaces. The theorem can be seen as an equivariant version of Schwede's rigidity theorem at the prime 2

On the Algebraic Classification of Module Spectra

Using methods developed by Franke, we obtain algebraic classification results for modules over certain symmetric ring spectra ($S$-algebras). In particular, for any symmetric ring spectrum $R$ whose graded homotopy ring $\pi_*R$ has graded global homological dimension 2 and is concentrated in degrees divisible by some natural number $N \geq 4$, we prove that the homotopy category of $R$-modules is equivalent to the derived category of the homotopy ring $\pi_*R$. This improves the Bousfield-Wolbert algebraic classification of isomorphism classes of objects of the homotopy category of $R$-modules. The main examples of ring spectra to which our result applies are the $p$-local real connective $K$-theory spectrum $ko_{(p)}$, the Johnson-Wilson spectrum E(2), and the truncated Brown-Peterson spectrum $BP$, for an odd prime $p$.Comment: 39 page

Does Active Management Benefit Endowment Returns?

We conduct a longitudinal analysis of the NACUBO Commonfund Study of Endowments (NCSE) results from 2006-2013 to evaluate if active management is related to higher endowment returns in U.S. equities over time. We also analyze the data to evaluate the endowment characteristics that are related to higher levels of performance over time.We find that active management for endowments is significantly positively related to higher returns net of fees from U.S. equity allocations over the evaluation period. In addition, endowments with CIOs or OCIOs are better able to earn incremental positive returns from active management than those without. Larger endowments are better able to earn incremental positive returns from active management than the smallest endowments but the effect appears to diminish as endowments increase in size

Topological Hochschild homology and the cyclic bar construction in symmetric spectra

The cyclic bar construction in symmetric spectra and B\"okstedt's original construction are two possible ways to define the topological Hochschild homology of a symmetric ring spectrum. In this short note we explain how to correct an error in Shipley's original comparison of these two approaches.Comment: v2: 7 pages; exposition improved, accepted for publication in Proceedings of the AM