# All Questions

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### Epsilon factors for tamely ramified extensions of local fields

Let $F$ be an unramified extension of $\mathbf{Q}_p$ of degree $n$, and let $K = F(\alpha)$ where $\alpha$ satisfies $\alpha^{p^n - 1} = -p$. I'm interested in the local $\varepsilon$-factors ...
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### Can we divide the following expression? If not, why not?

We have the following areas: $$\int_a^b f(x)dx=40$$ and $$\int_a^b g(x)dx=4$$ Question: can we calculate the following area? $$\int_a^b {f(x)\over g(x)}dx$$ If not why not?
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### Inequlities for averaging over partially ordered set

Let's start from a classical inequality: If $0\le a_1\le\cdots\le a_k$ and $0\le b_1\le\cdots\le b_k$ then $(a_1+\cdots+a_k)(b_1+\cdots+b_k)\le k(a_1b_1+\cdots+a_k b_k)$. It can be written also in ...
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### Pullback of a constant sheaf

Let $\varphi:X\to Y$ be a surjective morphism of schemes which are connected and of finite type. Let $A$ be an abelian group, $\mathscr{F}$ be the constant sheaf on $X$ with fibers $A$ and ...
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### How can I tell if the origin is in the convex hull of a set of points? [on hold]

I want to know how to tell if the origin is in the convex hull of a set of points. In particular, I really want to know a necessary condition for this in terms of which orthants the points are in. ...
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### Transfinite derivatives [migrated]

I don't know if this is exactly research level, as I am only starting college. But I feel like this is the best place to ask the question. We all know of 1st, 2nd, 3rd, nth derivatives. Is there a way ...
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### Finite dimension implies regularity

Let $\mathscr{D}'(\mathbb R)$ be the set of distributions on $\mathbb R$ and $X$ be a linear subspace of $\mathscr{D}'(\mathbb R)$, which is closed under translations, i.e., if $\varphi\in X$ and ...
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### Finding relations between invariant polynomials

Suppose I have an action of a linear reductive group ($GL(2,\mathbb{C})^2$ in this case) on a complex vector space (of dimension $16$) and I want to compute explicitly the ring of invariants of this ...
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### Institutional response to “Esquisse d'un programme”

It is well-known that Grothendieck's "esquisse d'un programme" was submitted in 1984 as part as the author's application for a permanent position of "Directeur de Recherche" at the C.N.R.S. (the main ...
Let $\mathfrak{M}$ be a countable transitive model of set theory, and consider HOD (the hereditarily ordinal definable elements of $\mathfrak{M}$). Let $x$ be an object $x \in HOD$. So $x$ is ...