The theory of motives is a conjectural theory proposed by Grothendieck that should provide a universal tool for studying the cohomology of varieties, and which is fundamentally linked to deep and important number-theoretic invariants such as L-functions. A number of mathematicians have proposed answers to the question "what is a motive?", and the aim of this course is to give an overview of several of the most prominent proposed constructions, and how each of these theories behave. A full course description is available here.

We will meet on Wednesdays at 12.00 in the maths department of University College London (room 505), beginning on the 10th of January. Each talk will last 75 minutes, with 15 minutes for questions and discussion at the end. If you would like to give a talk, please contact either Alex (alexander[dot]betts[at]kcl[dot]ac[dot]uk) or Chris (c[dot]birkbeck[at]ucl[dot]ac[dot]uk).

List of titles

Introduction

Systems of realisations

Pure motives

Applications to L-functions

1-motives

Theory: derived and triangulated categories

The derived category of motives

Theory: algebraic K-theory, Milnor K-theory and motivic cohomology

The Milnor conjecture and the (other) Bloch–Kato conjecture