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Results tagged with arithmetic-geometry
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user 21724
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
3
votes
Accepted
Inverse limit of finite flat morphisms
No (in general).
Take $S = \mathrm{Spec}(A)$ and $X_k = \mathrm{Spec}(A[T]/(T^2))$, with affine transition maps given by $T \mapsto f T$ for some $f \in A$. The limit $X$ is the spectrum of $A \oplus …
- 7,249
4
votes
Accepted
Relative approximation of morphisms
No (in general).
Let $A$ be a non-zero ring and let $S = \mathrm{Spec}(A[T]/(T^2))$. Let $M$ be a free $A$-module of infinite rank, viewed as an $A[T]/(T^2)$-module via the section $A[T]/(T^2) \righta …
- 7,249
3
votes
Accepted
Integral morphism between universally closed and separated schemes
Sure, by $(1)$ and $(4)$. Any integral morphism is affine by definition. If $f$ is an affine morphism with $f_* \mathcal{O}_X = \mathcal{O}_Y$, then $f$ is clearly an isomorphism.
- 7,249
13
votes
Accepted
Geometric intuition for Fontaine-Wintenberger?
First, the Fontaine-Winterberger isomorphism can also be recovered from a theorem of Deligne, namely Thm 2.8 here. Deligne showed that if two local fields $K_1$ and $K_2$ (possibly of different charac …
- 7,249