BCN Spring16 Workshop on Number Theory & K-theory
Minicourse on motivic cohomology of curves and varieties over a finite field
Co-ordinators
Satoshi Kondo
Description
We give some definitions of algebraic K-theory and
some definitions of motivic cohomology groups. We discuss some conjectures, known results, and some basic properties needed for the computation in the case of varieties over finite fields.
Secondly, we concentrate on the computation of motivic cohomology of curves over finite fields. We will give an outline of proof, using some known strong results. We then discuss some of my results (joint with Seidai Yasuda) on the computation of motivic cohomology and K-theory
of some higher dimensional varieties over a finite field.
Talks
- Introduction to motivic cohomology and algebraic $K$-theory (Satoshi Kondo)
- Motivic cohomology of curves and varieties over a finite field I. (Satoshi Kondo)
- Motivic cohomology of curves and varieties over a finite field II. (Satoshi Kondo)
References
S.Kondo-S.Yasuda ``On Two
higher Chow groups of schemes over a finite field" arxiv 1306.1607.
C.Weibel ``Algebraic K-Theory of rings of integers in local and global fields".
Handbook of K-theory, availble at
http://www.math.illinois.edu/K-theory/handbook/
