Birational invariants, purity and the Gersten conjecture Lectures at ...

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made possible by support from the Indo-French Centre for the Promotion of Advanced
Research (IFCPAR). I thank Steve Landsburg for producing an on-the-spot preliminary
write-up of the lectures.
Finally, I thank Bill Jacob and Alex Rosenberg for having given me an opportunity
to reflect on some basic concepts, and for the superb setting of the conference.
Notation
Given an abelian group A and a positive integer n, we write n A for the subgroup of
elements killed by n, and we write A/n for the quotient A/nA.
Given an integral domain A, we let qf(A) denote its fraction field.
In this paper, discrete valuation rings will be of rank one unless otherwise mentioned.
We let A n k , resp. Pn k
denote n-dimensional affine, resp. projective, space over a field
k.
If X is an irreducible variety, and p is a positive integer, we let X p denote the set of
all codimension p points of X, i.e. the set of points M ∈ X whose local ring O X,M is of
dimension p.