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Birational invariants, purity and the Gersten conjecture. (English) Zbl 0834.14009
Jacob, Bill (ed.) et al., $$K$$-theory and algebraic geometry: connections with quadratic forms and division algebras. Summer Research Institute on quadratic forms and division algebras, July 6-24, 1992, University of California, Santa Barbara, USA. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 58, Part 1, 1-64 (1995).
The paper under review is a nice survey on étale cohomology and unramified elements with respect to applications to the study of algebraic cycles and birational geometry. There are examples and exercises in order to give motivations for the sceptic reader. Mordell- Weil theorems for codimension 2 cycles and a rigidity theorem for unramified cohomology are explained as well.
For the entire collection see [Zbl 0812.00022].

##### MSC:
 14F20 Étale and other Grothendieck topologies and (co)homologies 14C25 Algebraic cycles 14E05 Rational and birational maps