Simultaneously vanishing higher derived limits

ON THE VANISHING OF DERIVED LOCAL HOMOLOGY MODULES

Let $R$ be a commutative Noetherian ring, $fa$ anideal of $R$ and $mathcal{D}(R)$ denote the derived category of$R$-modules. For any homologically bounded complex $X$, we conjecture that$sup {bf L}Lambda^{fa}(X)leq$ mag$_RX$. We prove thisin several cases. This generalize the main result of Hatamkhani and Divaani-Aazar cite{HD} for complexes.

Vanishing Scalar Invariant Spacetimes in Higher Dimensions

We study manifolds with Lorentzian signature and prove that all scalar curvature invariants of all orders vanish in a higher-dimensional Lorentzian spacetime if and only if there exists an aligned non-expanding, non-twisting, geodesic null direction along which the Riemann tensor has negative boost order.

Derived Equivalence and Non-vanishing Loci Ii

We prove a few cases of a conjecture on the invariance of cohomological support loci under derived equivalence by establishing a concrete connection with the related problem of the invariance of Hodge numbers. We use the main case in order to study the derived behavior of fibrations over curves.

Derived Equivalence and Non-vanishing Loci

The purpose of this note is to propose and motivate a conjecture on the behavior of cohomological support loci for topologically trivial line bundles under derived equivalence, to verify it in the case of surfaces, and to explain further developments. The reason for such a conjecture is the desire to understand the relationship between the cohomology groups of (twists of) the canonical line bun...

Scaling laws and vanishing viscosity limits in turbulence theory 1