3,027 research outputs found
Local duality for structured ring spectra
We use the abstract framework constructed in our earlier paper to study local
duality for Noetherian -ring spectra. In particular, we
compute the local cohomology of relative dualizing modules for finite morphisms
of ring spectra, thereby generalizing the local duality theorem of Benson and
Greenlees. We then explain how our results apply to the modular representation
theory of compact Lie groups and finite group schemes, which recovers the
theory previously developed by Benson, Iyengar, Krause, and Pevtsova.Comment: Revised version, to appear in Journal of Pure and Applied Algebr
The algebraic chromatic splitting conjecture for Noetherian ring spectra
We formulate a version of Hopkins' chromatic splitting conjecture for an
arbitrary structured ring spectrum , and prove it whenever is
Noetherian. As an application, these results provide a new local-to-global
principle in the modular representation theory of finite groups.Comment: Final version to appear in Mathematische Zeitschrif
Steady-state thermodynamics of non-interacting transport beyond weak coupling
We investigate the thermodynamics of simple (non-interacting) transport
models beyond the scope of weak coupling. For a single fermionic or bosonic
level -- tunnel-coupled to two reservoirs -- exact expressions for the
stationary matter and energy current are derived from the solutions of the
Heisenberg equations of motion. The positivity of the steady-state entropy
production rate is demonstrated explicitly. Finally, for a configuration in
which particles are pumped upwards in chemical potential by a downward
temperature gradient, we demonstrate that the thermodynamic efficiency of this
process decreases when the coupling strength between system and reservoirs is
increased, as a direct consequence of the loss of a tight coupling between
energy and matter currents.Comment: 6 pages, 2 figures, to appear in EP
Multiple tests for the performance of different investment strategies
In the context of modern portfolio theory, we compare the out-of-sample performance of 8 investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the traditional sample-based approach, several minimum-variance techniques, a shrinkage, and a minimax approach. In contrast to similar studies in the literature, we also consider shortselling constraints and a risk-free asset. We provide a way to extend the concept of minimum-variance strategies in the context of short-selling constraints. A main drawback of most empirical studies on that topic is the use of simple-testing procedures which do not account for the effects of multiple testing. For that reason we conduct several hypothesis tests which are proposed in the multiple-testing literature. We test whether it is possible to beat a trivial strategy by at least one of the non-trivial strategies, whether the trivial strategy is better than every non-trivial strategy, and which of the non-trivial strategies are significantly outperformed by naive diversification. In our empirical study we use monthly US stock returns from the CRSP database, covering the last 4 decades. --Asset allocation,Certainty equivalent,Investment strategy,Markowitz,Multiple tests,Naive diversification,Out-of-sample performance,Portfolio optimization,Sharpe ratio
Stratification and duality for homotopical groups
We generalize Quillen's -isomorphism theorem, Quillen's stratification
theorem, the stable transfer, and the finite generation of cohomology rings
from finite groups to homotopical groups. As a consequence, we show that the
category of module spectra over is stratified
and costratified for a large class of -local compact groups
including compact Lie groups, connected -compact groups, and -local
finite groups, thereby giving a support-theoretic classification of all
localizing and colocalizing subcategories of this category. Moreover, we prove
that -compact groups admit a homotopical form of Gorenstein duality.Comment: Corrected discussion of Chouinard's theorem for homotopical groups;
accepted for publication in Advances in Mathematic
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