We formulate and prove an analogue of the noncommutative Iwasawa main conjecture for `-adic Lie extensions of a separated scheme X of finite type over a finite field of characteristic prime to `.

A conceptual proof is given of the fact that the coefficients of the characteristic series of the U-operator acting on families of overconvegent modular forms lie in the Iwasawa algebra.

Finding a good metric over the input space plays a fundamental role in machine learning. Most existing techniques assume the Mahalanobis metric without incorporating the geometry of Pn, the space of n×n symmetric positive-definite (SPD) matrices, which leads to difficulties in the optimization procedure used to learn the metric. In this paper, we introduce a novel algorithm to learn the Mahalan...

This article introduces the problem of finding intrinsic torsion varieties associated to G -structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures are analysed on the Iwasawa manifold.

Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the dual pair of σ-models defined by the double SO(3,1) in the Iwasawa decomposition .