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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

4 votes
0 answers
385 views

Intuition behind Artin/Grothendieck's Riemann existence theorem

The following result is due to Grothendieck and Artin and can be found in SGA 1. Let $X$ be a normal scheme of finite type over $\mathbb{C}$. Let $\mathfrak{X}'$ be a normal complex analytic space, to …
6 votes
1 answer
356 views

Infinitely many primes $p \in \mathbb{Z}$ where reduced curve $E/\mathbb{F}_p$ has Hasse inv...

Let $E$ be an elliptic curve defined over $\mathbb{Q}$, and fix a Weierstrass equation for $E$ having coefficients in $\mathbb{Z}$. Are there infinitely many primes $p \in \mathbb{Z}$ such that the re …