Homepage: Boris Zilber (original) (raw)

Teaching

Graduate Courses

Elements of Geometric Stability Theory (pdf)

_____________________________________________________________________________

Zariski Geometries

• Cambridge University Press, 2010

Zariski Geometries are abstract structures in which a suitable generalisation of Zariski topology makes sense. Algebraic varieties over an algebraically closed field and compact complex spaces in a natural language are examples of Zariski geometries. The main theorem by Hrushovski and the lecturer states that under certain non-degeneracy conditions a 1-dimensional Zariski geometry can be identified as an algebraic curve over an algebraically closed field. The proof of the theorem exhibits, as a matter of fact, a way to develop algebraic geometry from purely geometric abstract assumptions not involving any algebra at all. Recent works in model theory of complex manifolds, differential fields and non-commutative geometry point to exciting perspectives for the theory.