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28,137 questions with no upvoted or accepted answers
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### The exponent of Ш of $y^2 = x^3 + px$, where $p$ is a Fermat prime

For $d$ a non-zero integer, let $E_d$ be the elliptic curve $$E_d : y^2 = x^3+dx.$$ When we let $d$ be $p = 2^{2^k}+1$, for $k \in \{1,2,3,4\}$, sage tells us that, conditionally on BSD,  \# Ш(E_p)...
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### Normalizers in symmetric groups

Question: Let $G$ be a finite group. Is it true that there is a subgroup $U$ inside some symmetric group $S_n$, such that $N(U)/U$ is isomorphic to $G$? Here $N(U)$ is the normalizer of $U$ in $S_n$. ...
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### Constructing non-torsion rational points (over Q) on elliptic curves of rank > 1

Consider an elliptic curve $E$ defined over $\mathbb Q$. Assume that the rank of $E(\mathbb Q)$ is $\geq2$. (Assume the Birch-Swinnerton-Dyer conjecture if needed, so that analytic rank $=$ algebraic ...
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### Dualizing the Notion of Topological Space

$\require{AMScd}$ Defining a topological space on a set $X$ is equivalent to designating certain subobjects of $X$ in ${\bf Set}$ (monomorphisms into $X$ up to equivalence) as open. The requirements ...
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Given $A,B\in {\Bbb Z}^2$, write $A \leftrightarrows B$ if the interior of the line segment AB misses ${\Bbb Z}^2$. For $r>0$, define $S_r:=\{ \{A, B\} | A,B\in {\Bbb Z}^2,||A||<r,||B||<r, |... 0answers 1k views ### What did Gelfand mean by suggesting to study “Heredity Principle” structures instead of categories? Israel Gelfand wrote in his remarkable talk "Mathematics as an adequate language (a few remarks)", given at "The Unity of Mathematics" Conference in honor of his 90th birthday, the following ... 0answers 1k views ### Are there periodicity phenomena in manifold topology with odd period? The study of$n$-manifolds has some well-known periodicities in$n$with period a power of$2$:$n \bmod 2$is important. Poincaré duality implies that odd-dimensional compact oriented manifolds ... 0answers 2k views ### To what extent does Spec R determine Spec of the Witt vector ring over R? Let$R$be a perfect$\mathbb{F}_p$-algebra and write$W(R)$for the Witt ring [i.e., ring of Witt vectors -- PLC] on$R$. I want to know how much we can deduce about$\text{Spec } W(R)\$ from ...

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