Rational fixed points for linear group actions
| dc.creator | Corvaja, Pietro | |
| dc.date | 2006-10-23 | |
| dc.date | 2007-08-16 | |
| dc.date.accessioned | 2026-07-07T08:23:49Z | |
| dc.date.available | 2026-07-07T08:23:49Z | |
| dc.description | Let $k$ be a finitely generated field, let $X$ be an algebraic variety and $G$ a linear algebraic group, both defined over $k$. Suppose $G$ acts on $X$ and every element of a Zariski-dense semigroup $Γ\subset G(k)$ has a rational fixed point in $X(k)$. We then deduce, under some mild technical assumptions, the existence of a rational map $G\to X$, defined over $k$, sending each element $g\in G$ to a fixed point for $g$. The proof makes use of a recent result of Ferretti and Zannier on diophantine equations involving linear recurrences. As a by-product of the proof, we obtain a version of the classical Hilbert Irreducibility Theorem valid for linear algebraic groups. | |
| dc.description | 35 pages, Plain Tex. A gap in the previous proof of Theorem 1.2 overcome, plus minor changes. Thanks to J. Bernik and the referee | |
| dc.identifier | https://arxiv.org/abs/math/0610661 | |
| dc.identifier | http://arxiv.org/abs/math/0610661 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136136 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G35; 12E25; 11E99 | |
| dc.title | Rational fixed points for linear group actions | |
| dc.type | text |