# All Questions

100,158 questions
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### Partial well-ordering of formulas

Given a theory $T$, for arbitrary formulas $φ$ and $ψ$ that provably in $T$ denote an ordinal, set $[φ]_T < [ψ]_T$ iff provably in $T$, the ordinal denoted by $φ$ is less than the ordinal denoted ...
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### rank of Jacobian of Fermat curve and Chabauty-Coleman method

Consider the fermat curve $F(p)$ over $\mathbb Q$ which is the projective closure of $X^p+Y^p=1$ inside projective plane, where $p$ is a prime number and without loss of generality we assume $p>2$. ...
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### Quotient of a smooth projective surface by an involution

Is the quotient of a smooth complex projective surface by an involution projective? Suppose the quotient happens to be smooth; does that change the situation?
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### Translation of Soergel's 1990 paper on category O

Is there any English translation for the folowing paper of Soergel? Kategorie $\mathcal{O}$, perverse Garben, und Moduln über den Koinvarianten zur Weylgruppe, J. Amer. Math. Soc. 3 (1990), 421-445,...
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### Lower-bound probability of non-centered quadratic form

Let $X\sim N(\mu,\sigma^2I)\in \mathbb{R}^n$ be a non-centered ($\mu\neq 0$) Gaussian vector with independent coordinates. I'm wondering if there is any sharp lower bound of the following probability: ...
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### Sources of derived schemes in geometric representation theory

What are some derived schemes naturally arising in geometric representation theory? Some examples include: Steinberg scheme Hilbert scheme Moduli stack of local systems. Now, this looks like a ...
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### A clarification of an argument in “Perfectoid spaces”

The page 50 of (the arXiv version of) the above-mentioned paper of P. Scholze says "Now the Poincare duality pairing implies that $H^i(Y_{\mathbb{C}_p, et}, \bar{\mathbb{Q}}_l)$ is a direct summand of ...
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### Are Chain Complexes Related to the Tangent Bundle Construction?

For a scheme $X$ over $\text{Spec}(K)$, we can consider maps $\text{Sch}(\text{Spec}(K[d] / d^2), X)$, which we can think of as the tangent bundle over $X$. A map $\text{Spec}(K) \rightarrow S$ picks ...
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### Absolute oscillator in Langton's Ant

We have a simple (or single) block of Langton's Ants colony which includes two ants looking in the same direction. Their positions can be interpreted as knight's walk. The distances between each next ...
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### Perform a univariate integral, involving a Gauss hypergeometric function

This is a follow-up question to the one posed in Compute the two-fold partial integral, where the three-fold full integral is known . (I hope that doing so is viewed as a legitimate step. If not so, I ...
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### Factoring $\frac{1}{1-rx}$ into an infinite products of polynomials

I am looking for examples of sequences of polynomials $(p_{k}(x))_{k=1}^{\infty}$ with positive integer coefficients where $p_{k}(0)=1$ for all $k\geq 1$ and where there is a positive integer $r$ ...
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### Finding the minimum sum of a subset of entries of a given matrix with combinatorial constraints

Given a matrix $M\in\mathbb{N}^{n\times n}$, let $Z$ be the set of all the $M$'s entry subsets $S$ such that (i) no two entries of $S$ are on the same row or column of $M$ and (ii) $|S|=n$. Clearly we ...
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### Reference question: $C^1$ estimate for a stable minimal surface
I am looking for an answer/reference to the following question: Let $(M,g)$ be a complete Riemannian manifold and $\Sigma\subset M$ a closed, stable minimal surface. Is it possible to prove $C^1$ ...
### Twisted spin-bordism invariant and a possible Postnikov square from $d=2$ to $d=5$
This is a follow up more advanced question following Twisted spin bordism invariants in 5 dimensions. We follow the definitions in the earlier post. I had discussed my computation of  \Omega_5^{...