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Mixed motives and algebraic K-theory. (Almost unchanged version of the author’s habilitation at Univ. Regensburg 1988). (English) Zbl 0691.14001
Lecture Notes in Mathematics, 1400. Berlin etc.: Springer-Verlag. xi, 246 p. DM 37.00 (1990).
This book is an almost unchanged version of the author’s Habilitationsschrift at the University of Regensburg that has been reviewed previously (1988; Zbl 0661.14001). The author has only made some minor corrections and added three appendices.
Appendix A reproduces a letter from S. Bloch to the author, which shows that the homological formulation of the Hodge conjecture for singular varieties which the author states in section 7 of the book is the only one possible. S. Bloch gives a counterexample to the corresponding cohomological conjecture. In Appendix B an example by C. Schoen is given of the following phenomenon: A smooth projective surface V over a field k satisfiying:
(i) \(\text{rank}(\text{Ker}: CH_ 0(V)_{\deg 0}\to \text{Alb}_ V(k))=\infty\);
(ii) \(V\) cannot be obtained by base changing a variety \(V'/k'\) for a field \(k'\subset k\) with \(\text{trans}.\deg.(k/k')>0.\)
The third appendix contains some remarks and complements written by the author in 1989.
Reviewer: Fu-an Li

MSC:
14A20 Generalizations (algebraic spaces, stacks)
14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
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