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Can someone give me an example of a non-quasi-compact morphism of schemes which arises naturally in the field of Algebraic Number Theory?

Your second question is answered affirmatively by EGA IV_2 Corollary 6.5.2, which references EGA IV_1 $\S0$ 17.3.3(i). Here you only need to assume that $f: X \rightarrow Y$ is a flat morphism of loca …

I am not sure if this is what the OP really wants, but this is the proof I had in mind. Theorem. Let $(A,m)$ be a local ring which is obtained by localizing a finitely generated $k$-algebra where $k$ …

I was reading Hodges' "Model Theory" Chapter 8 a propos existentially closed models of $\forall_2$ theories in a countable first order language $L$. He extends the proof of the omitting type theorem …

Let $V$ be a variety over $\mathbb{C}$ and suppose $O$ is a singular point of $V$. Are there conditions on $(V,O)$ such that a versal deformation $W$ of $(V,O)$ has only quasi-ordinary singularities. …

This is a re-post on a previous question I asked. My first question was too vague to warrant detailed responses. Really, I have two specific questions to ask. 1) Let $\sigma = (A; \{0,1\}; +, \times …

No, but Serre proved that for noetherian local rings having finite global dimension is the same as being regular. So, choose any non-regular local ring which at the same time an integral domain such …

A morphism of schemes which is formally unramified, universally closed, and a monomorphism is a closed immersion. Is it possible to characterize morphisms which are formally etale and universally clos …