§1. Geometry of finite type and review of CR-extension theory . . . . .2. §2. Identification of CR vector fields and of Segre varieties . . . . . . . . . .4. §3. Segre varieties and extrinsic complexification . . . . . . . . . . . . . . . . . . . .10. §4. Segre sets and iterated complexifications . . . . . . . . . . . . . . . . . . . . . . . . .12. §5. Segre varieties and conjugate Segre variet...

Let k be a totally real field, and let A/k be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphism rings is non-trivial and is defined over k. Then the only strictly compatible families of abstract, absolutely irreducible representations of Gal(k/k) coming from A are tensor products of Tate twists of symmetric powers of two-dimensional λ-adic represent...

Let V be a p-adic representation of the absolute Galois group G of Qp that becomes crystalline over a finite tame extension, and assume p 6= 2. We provide necessary and sufficient conditions for V to be isomorphic to the p-adic Tate module Vp(A) of an abelian variety A defined over Qp. These conditions are stated on the filtered (φ,G)module attached to V . 2000 Mathematics Subject Classificatio...

Sustainability is getting popular for many engineering applications from packaging to textiles, energy electronics. Since renewable, environmental friendly sources lowers the negative impacts of end product on ecology, sustainability studies generally start with raw materials. The electronic materials has gained importance because limited amount resources and increasing costs as well restrictio...