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Dear Daniel, here is a detailed explanation, respectfully following the sacred texts (EGA or Hartshorne). a) First of all, $\mathbb A^{n+1}_{\mathbb Z}$ has no origin, despite our classical intuition …

I find Hodge theory pretty scary stuff with its compact inclusions of Sobolev spaces, pseudodifferential operators and parametrixes for elliptic differential operators. However it is very easy to use …

Consider $X= Spec( \mathcal O_K)$ and an open subset $ U \subset X \quad (U\neq \emptyset, X)$. Take two copies $U'\subset X',U''\subset X''$ of the above and glue them along the identity $U'\to U …

I certainly don't claim that I can answer your questions authoritatively , but here are two small remarks. 1) Samuel's book is certainly an excellent guess: it is actually the only textbook in Fr …

a) Conceptually an algebraic topologist should be interested in étale cohomology, because it answers a very naïve question: given an algebraic variety over $\mathbb C$, how do I calculate algebraicall …

Dear Olivier, in line with the more advanced nature of this site, let me give an example of a less elementary nature. Consider a compact Riemann surface $X$ of genus 2 and on it stable vector bundles …