Lecture

Affine Algebraic Sets

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In course

MATH-328: Algebraic geometry I - Curves

Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...

Description

This lecture introduces affine algebraic sets, starting with the definition of affine space and algebraic sets over a field. It covers the concept of hypersurfaces, affine planes, and elliptic curves, illustrating examples and properties of algebraic subsets. The lecture also discusses the relationship between ideals and algebraic sets, emphasizing the importance of the ground field being algebraically closed. Additionally, it explores the notion of Noetherian rings and modules, showcasing the finitely generated ideals and their corollary in algebraic varieties.

Instructor

Dimitri Stelio Wyss

I did my PhD under the supervision of Tamas Hausel at EPFL and the Institue of Science and Technology Austria . From 2017-2019 I was a postdoctoral researcher at the Sorbonne University Paris 6 with François Loeser. Since September 2019 I hold the chair of arithmetic geometry at EPFL as a tenure track assistant professor. For more information see my CV.I work in algebraic and arithmetic geometry. My research uses ideas from p-adic and motivic integration to study the interplay between geometric and arithmet

Official source

Ontological neighbourhood

Mathematics

Algebra: Abstract algebra

Geometry: Algebraic geometry

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