The Étale Homology and the Cycle Maps in Adic Coefficients

In this article, we define the $ℓ$-adic homology for a morphism of schemes satisfying certain finiteness conditions. This homology has these functors similar to the Chow groups: proper push-forward, flat pull-back, base change, cap-product, etc. In particular, on singular varieties, this kind of $ℓ$-adic homology behaves much better than the classical $ℓ$-adic cohomology. As an application, we give a much easier approach to construct the cycle maps for arbitrary algebraic schemes over fields. And we prove that these cycle maps kill the algebraic equivalences and commute with the Chern action of locally free sheaves.     

ENHANCED BLOCK-SPARSE SIGNAL RECOVERY PERFORMANCE VIA TRUNCATED e2/e1-2 MINIMIZATION

In this paper, we investigate truncated $ℓ_2/ℓ_{1−2}$ minimization and its associated alternating direction method of multipliers (ADMM) algorithm for recovering the block sparse signals. Based on the block restricted isometry property (Block-RIP), a theoretical analysis is presented to guarantee the validity of proposed method. Our theoretical results not only show a less error upper bound, but also promote the former recovery condition of truncated ℓ₁₋₂ method for sparse signal recovery. Besides, the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.