Algebra Seminar  RSS

12/07/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building
, 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:

  1. 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.
  2. 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

Current organizer: Gustavo Granja

CAMGSD FCT