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Zariski geometry

Zariski geometry is a structure defined by Boris Zilber. See his book

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.

Created on June 19, 2011 21:32:49 by Zoran Škoda (212.15.172.187)