Transcendental Aspects of Algebraic Cycles: Proceedings of the Grenoble Summer School, 2001

Contents......Page page000004.djvu
List of participants page......Page page000007.djvu
Preface......Page page000010.djvu
Acknowledgements......Page page000018.djvu
Part I. Introductory material......Page page000020.djvu
Introduction......Page page000022.djvu
1.1. Chow varieties......Page page000023.djvu
1.2. The Euler-Chow series of Chow varieties......Page page000029.djvu
1.3. Some open problems, interesting relations for the Euler-Chow series, and the total coordinate ring......Page page000056.djvu
References......Page page000061.djvu
2.1. Basic notions......Page page000063.djvu
2.2. Chow varieties and cycle spaces......Page page000069.djvu
2.3. Defining Lawson homology......Page page000076.djvu
References......Page page000089.djvu
Part II. Lawson (co)homology......Page page000092.djvu
3.1. Introduction......Page page000094.djvu
3.2. Topological properties of algebraic cycles......Page page000097.djvu
3.3. Lawson homology......Page page000106.djvu
3.4. First applications......Page page000111.djvu
3.5. (Colimits of) mixed Hodge structures on Lawson homology......Page page000117.djvu
3.6. Intersection theory......Page page000125.djvu
3.7. Morphic cohomology......Page page000131.djvu
References......Page page000136.djvu
Part III. Motives and motivic cohomology......Page page000140.djvu
4.1. Lecture 1: Grothendieck's construction of motives......Page page000142.djvu
4.2. Lecture 2: conjectures and results on motives (main points)......Page page000156.djvu
4.3. Lecture 3: conjectures and results on motives (continued)......Page page000165.djvu
4.4. Lecture 4: Chow-Künneth decomposition for elliptic modular varieties......Page page000176.djvu
References......Page page000186.djvu
Introduction......Page page000190.djvu
5.1. Definitions and basic constructions......Page page000191.djvu
5.2. Localization and Mayer-Vietoris sequences......Page page000197.djvu
5.3. Gersten resolution for higher Chow groups......Page page000198.djvu
5.4. K-theory and the motivic spectral sequence......Page page000201.djvu
5.5. Some explicit computations......Page page000203.djvu
References......Page page000213.djvu
Part IV. Hodge theoretic invariants of cycles......Page page000216.djvu
6.1. Lecture 1: the statement and some standard examples......Page page000218.djvu
6.2. Lecture 2: a geometric approach......Page page000235.djvu
6.3. Lecture 3: the method via the diagonal class......Page page000239.djvu
6.4. Appendix: the Tate conjecture, absolute Hodge cycles, and some recent developments......Page page000245.djvu
References......Page page000250.djvu
7.1. Normal functions......Page page000254.djvu
7.2. Griffiths's theorem......Page page000262.djvu
7.3. The theorem of Green-Voisin......Page page000267.djvu
7.4. Nori's connectivity theorem......Page page000270.djvu
7.5. Sketch of proof of Nori's theorem......Page page000274.djvu
7.6. Applications of Nori's theorem......Page page000285.djvu
7.7. Appendix: Deligne cohomology......Page page000290.djvu
References......Page page000292.djvu
Introduction......Page page000295.djvu
8.1. Koszul cohomology for open complete intersections......Page page000296.djvu
8.2. Beilinson's Hodge and Tate conjectures......Page page000300.djvu
8.3. Noether-Lefschetz problem for K₂ of open surfaces......Page page000304.djvu
References......Page page000308.djvu