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Results tagged with arithmetic-geometry
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user 115211
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
8
votes
Accepted
Finite subgroup scheme and Neron model of an abelian variety
In general the scheme $\mathcal A[l]_{\mathcal O}$ is not finite because of the following lemma.
Let $f:X\to Y$ be a separated quasi-finite flat morphism of noetherian schemes. Then it is finite …
- 2,841
3
votes
Accepted
Extending section of étale morphism of adic spaces
The statement is correct and here is one way to prove it. The slogan is that "finite etale extensions of $k(x)$ and $\widehat{k(x)}$ are the same for "quasi-complete" fields $k(x)$" (this is a toy exa …
- 2,841
2
votes
Rank of $\mathbb{Z}_{p}$-module $H_{et}^{i}(X,\mathbb{Z}_{p}(r))$
The first question has a positive answer. This is essentially a combination of two very different finiteness results and quite specific to local fields. In what follows, I will explain the argument fo …
- 2,841
8
votes
Curves over number fields with everywhere good reduction
Do we expect the existence of (quadratic?) number fields $K \neq \Q$ such that the assertion $A_K$ does not hold (so that in particular, there is no smooth projective curve of genus $>0$ over $K$ w …
- 2,841
7
votes
Accepted
Nearby cycles and extension by zero
The statement is false without proper assumption.
Consider any "degeneration of a smooth elliptic curve to a nodal curve" and delete a singular point in a special fibre. This will give you a counter …
- 2,841