12/07/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building
Bjorn Poonen, Massachussetts Institute of Technology
Existence of rational points on smooth projective varieties
Let $k$ be a finite extension of the field $\mathbb{Q}$. We prove results including:
- If there is an algorithm to decide whether a smooth projective $k$-variety has a $k$-point, then there is an algorithm to decide whether an arbitrary $k$-variety has a $k$-point.
- If there is an algorithm to decide whether a smooth projective 3-fold has a $k$-point, then there is an algorithm to compute $X(k)$ for any curve $X$ over $k$.
See also
http://math.mit.edu/~poonen/papers/chatelet.pdf
