From Sheaf Cohomology to the Algebraic de Rham Theorem

Let X be a smooth complex algebraic variety with the Zariski topology, and let Y be the underlying complex manifold with the complex topology. Grothendieck's algebraic de Rham theorem asserts that the singular cohomology of Y with complex coefficients can be computed from the complex of sheaves of algebraic differential forms on X. This article gives an elementary proof of Grothendieck's algebraic de Rham theorem, elementary in the sense that we use only tools from standard textbooks as well as Serre's FAC and GAGA papers.Comment: 53 pages; this version replaces an earlier version submitted in August 2013. Some misprints have been correcte

Analysis of thin-film structures with nuclear backscattering and x-ray diffraction

Backscattering of MeV ^(4)He ions and Seemann-Bohlin x-ray diffraction techniques have been used to study silicide formation on Si and SiO_2 covered with evaporated metal films. Backscattering techniques provide information on the composition of thin-film structures as a function of depth. The glancing-angle x-ray technique provides identification of phases and structural information. Examples are given of V on Si and on SiO_2 to illustrate the major features of these analysis techniques. We also give a general review of recent studies of silicide formation