Schemes And Their Functors Of Points

The central concept of modern algebraic geometry is the notion of a scheme, due to Grothendieck. The basic idea is to view arbitrary commutative rings as geometric objects. They can be used to build more complicated geometric objects called schemes. It is often useful to view a scheme as a presheaf on the category of schemes or just on the category of rings. The research question for the project is: Which presheaves are represented by a scheme?

Alexander Lai De Oliveira

University Of Adelaide

Alexander is a second-year student completing a Bachelor of Mathematical Sciences degree at the University of Adelaide. His current interest is algebraic geometry, a rich and diverse subject with many specialisations.The central concept of modern algebraic geometry is the notion of a scheme, due to Grothendieck. The basic idea is to view arbitrary commutative rings as geometric objects. They can be used to build more complicated geometric objects called schemes. It is often useful to view a scheme as a presheaf on the category of schemes or just on the category of rings. The research question for the project is: Which presheaves are represented by a scheme?

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