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Results tagged with reference-request
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user 6074
This tag is used if a reference is needed in a paper or textbook on a specific result.
12
votes
Ways to prove the fundamental theorem of algebra
Here is a variant of d'Alembert's argument using the minimum of $|p(z)|$. It has the advantage that it proves more generally the Gelfand-Mazur theorem (usually proved by complex analysis): Any Banach …
21
votes
0
answers
2k
views
Cartan–Oka vanishing in one variable without $\overline{\partial}$?
This is a literature question, about possible proofs of some very basic results in complex analysis.
Some key facts about holomorphic functions are proved via reduction to smooth functions, using $\ov …
- 21.3k
31
votes
1
answer
2k
views
Topology on space of hyperfunctions
This is a reference request, coming from someone with little knowledge of hyperfunctions:
Which methods have been used to endow the space of hyperfunctions $\mathcal B(\mathbb R)$ with something like …
- 21.3k
260
votes
Accepted
What are "perfectoid spaces"?
Update: The lecture notes of the CAGA lecture series on perfectoid spaces at the IHES can now be found online, cf. http://www.ihes.fr/~abbes/CAGA/scholze.html.
It seems that it's my job to answer thi …
- 21.3k
6
votes
Accepted
Derived category of abelian sheaves on a site equivalent to sheaves on the derived category ...
It's true in any $1$-topos for hypercomplete sheaves, see Theorem 2.1.2.2 in Spectral Algebraic Geometry.
- 21.3k
12
votes
Accepted
Does $0\to I\to\mathrm{Gal}_K\to\mathrm{Gal}_k\to 0$ always split?
Good question! Let me try to guess what Gabber had in mind there. (Note that he only says "known" (to him), not "well-known"...)
The claim is that the extension splits. Note that to prove this, we are …
- 21.3k
29
votes
Accepted
Derived categories and $\infty$-categories necessary for condensed mathematics
There are several questions (implicit) here.
In the texts as they are written, how much knowledge on derived categories (as triangulated categories, or as stable $\infty$-categories) is assumed?
Doe …
- 21.3k