Cours spécialisé (GA, GT, TA)

How homotopy theory helps algebraic geometry

Maria Yakerson

Contact : yakerson à imj-prg.fr

Notes de cours : Notes will be updated during the course

Langue du cours : english

Présentation

Motivic homotopy theory, created in the end 90s by F. Morel and V. Voevodsky and vastly developed since, aims to apply methods from homotopy theory to objects in algebraic geometry. In this course, we will have an introduction into motivic homotopy theory and then discuss example of such applications, such as classification problems for vector bundles on algebraic varieties.

Contenu

motivic homotopy theory
obstruction theory
unstable homotopy theory
classification of vector bundles

Prérequis

The prerequisites are: sheaf cohomology, scheme theory, homotopy theory, basic category theory. I recommend taking the courses Schemas I and Homotopie II.

Bibliographie

A. Asok and J. Fasel. Vector bundles on alg varieties. https://arxiv.org/abs/2111.03107
A. Asok. Algebraic geometry from an A^1-homotopic viewpoint. https://dornsife.usc.edu/aravind-asok/wp-content/uploads/sites/213/2023/06/MATH614.S21.pdf
T. Brazelton. Unstable motivic homotopy theory. https://github.com/tbrazel/math266-motivic/blob/main/main.pdf