Projective modules and A1-homotopy theory

May 5 to May 9, 2014

at the

American Institute of Mathematics, Palo Alto, California

organized by

Aravind Asok, Jean Fasel, and Satyagopal Mandal

Original Announcement

This workshop will be devoted to studying recent interactions between the classical theory of projective modules and $A^1$-homotopy theory.

Recent work of F. Morel provides an analog of Steenrod's classification of topological vector bundles in terms of homotopy classes of maps to a Grassmannian. More precisely, he identifies the set of isomorphism classes of projective modules of fixed rank over a smooth affine algebra $R$ with the maps in the $A^1$-homotopy category between the associated affine scheme Spec $R$ and an algebro-geometric Grassmannian. This result provides a dictionary by which to translate topological results about vector bundles to results about projective modules. The goal of this workshop is to introduce practitioners of the theory of projective modules to modern ideas about $A^1$-homotopy theory and vice versa.

During the workshop, we will focus on the following questions/problems:

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:
On the number of generators of ideals in polynomial rings
Intersection Multiplicity of Serre in the Unramified Case
R-equivalence and A^1-connectedness in anisotropic groups