MathOverflow

I'm a topologist, not an algebraic geometer, so I apologize if this question is either naive or awkwardly framed. Throughout, I'll work over the complex numbers and use the language of varieties.
Let $X$ be the total space of the tautological line bundle over $\mathbb{P}^1$ and let $Y = \mathbb{P}^1 \times \mathbb{A}^1$ be the total space of the trivial line bundle over $\mathbb{P}^1$. I'm pretty sure that $X$ is not isomorphic to $Y$ as a variety...

I would like to have your comments, opinions, and suggestions on a proposal of an autonomous generator of prime numbers.
This proposal is based on the arithmetic framework UNI (Unity Normalization Interface) in which the unit 1 is decomposed into five fundamental dimensions A, B, C, D, E satisfying five independent constraints:...

Conjecture. Let $s(n, k)$ denote the unsigned Stirling numbers of the first kind, and let $p$ be an odd prime such that $p \notin \{3, 7, 11\}$.
For any integer $n \ge 1$, let $n = (d_k d_{k-1} \dots d_1 d_0)_p$ be its base-$p$ expansion, where $k = \lfloor \log_p(n) \rfloor$. Then$$v_p(|s(n+1, 2)|) = v_p(n!) - \lfloor \log_p(n) \rfloor + \Delta_p(n)$$...

Let $G$ be a simple $p$-divisible group over $\mathbb{Z}_p$ (arising from a formal group over $\mathbb{Z}_p$, so connected), and let $V := T_p(G)\otimes_{\mathbb Z_p}\mathbb Q_p$be its Tate module. Let $\rho : G_{\mathbb Q_p}=\operatorname{Gal}(\bar...