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Results tagged with reference-request
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user 115211
This tag is used if a reference is needed in a paper or textbook on a specific result.
5
votes
1
answer
450
views
Tate conjecture and finiteness of Brauer group
What is the exact relation between the Tate conjecture for divisors on $X$ and finiteness of the Brauer group of $X$? And what is the reference for these relations?
More precisely, let $X$ be a smooth …
- 2,841
17
votes
Accepted
Example of a smooth projective family of varieties in characteristic $p$ where the Hodge num...
Update: The details of this construction are now available in my blog post with Sean Cotner on Thuses.
I was recently interested in exactly the same question. But I failed to find any reference where …
- 2,841
12
votes
Smoothen a nodal curve
This is correct that you can always "deform" a nodal curve into a smooth one. A good reference for this fact is Corollary $7.11$ in these notes by Talpo and Vistoli.
UPD: As Qixiao points out Talpo …
- 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
8
votes
0
answers
394
views
Foundational Questions on Adic Spaces
There are some foundational questions on adic spaces that I can't find in the literature. It seems that these questions are pretty natural, so I guess that an answer should be known to the experts in …
- 2,841
12
votes
3
answers
886
views
Chow Groups of varieties over number fields
I believe that there is a conjecture that for any smooth projective variety $X$ over a number field $K$, its Chow groups $CH^i(X)$ (or at least $CH^i(X)\otimes_{\mathbf Z} \mathbf Q$) are finitely gen …
- 2,841