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7 votes
0 answers
140 views

Average number of $\mathbb{F}_p$-points over twists of a variety

Let $p \gg 1$ be a sufficiently large prime. I recently stumbled across a fascinating fact about the number of $\mathbb{F}_p$-points on elliptic curves over finite fields. Specifically, we have: Fact ...
Ashvin Swaminathan's user avatar
1 vote
0 answers
173 views

Levi decompositions of k-rational points of linear algebraic groups

Let $k$ be a field with characteristic zero and $G$ be a (connected or not) linear algebraic group defined over $k$. We know that $G$ has a Levi decomposition i.e., $G=R_u(G)\rtimes L$, where $R_u(G)$ ...
m07kl's user avatar
  • 1,702
2 votes
1 answer
123 views

F-points of product of closed subgroups vs. product of F-points, F a local field, reference?

Let $F$ be a finite extension of $\mathbb Q_p$, where p is an odd prime. Let $G$ be a connected reductive group defined over $F$. Let $M, H$ be closed $F$-subgroups of $G$ (in particular, I'm ...
Jerrod Smith's user avatar