Download Algebraic Geometry: A Volume in Memory of Paolo Francia by Paolo Francia, Fabrizio Catanese, C. Ciliberto, A. Lanteri, PDF

By Paolo Francia, Fabrizio Catanese, C. Ciliberto, A. Lanteri, C. Pedrini, Mauro Beltrametti

Eighteen papers, many drawing from shows on the September 2001 convention in Genova, conceal a variety of algebraic geometry. specific awareness is paid to raised dimensional forms, the minimum version application, and surfaces of the overall variety. a listing of Francia's courses is integrated. individuals contain mathematicians from Europe, the U.S., Japan, and Brazil

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1. 2. Extensions 32 2. 1. 2. 3. Hodge conjecture for singular varieties 38 3. 1. 2. 3. 4. Local-to-global properties 45 4. 1. 2. Coniveau filtration 49 Algebraic Geometry. A Volume in Memory of Paolo Francia M. C. Beltrametti, F. Catanese, C. Ciliberto, A. Lanteri, C. ) © Walter de Gruyter 2002 26 L. 3. 4. K-cohomology and motivic cohomology 5. 1. 2. Srinivas’ example 51 53 55 55 56 0. Introduction Let X be an algebraic C-scheme. The singular cohomology groups H ∗ (X, Z(·)) carry a mixed Hodge structure, see [11, III].

Deligne who also provided me with advice that helped on several portions of the manuscript. On algebraic 1-motives related to Hodge cycles 31 I am grateful also to S. Bloch, O. Gabber, H. Gillet, M. Hanamura, U. Jannsen, M. Levine, J. D. Lewis, J. Murre, A. Rosenschon, M. Saito, C. Soulé and V. Voevodsky for discussions on some matters treated herein. Finally, I would like to thank Paolo Francia for his helpful insight and invaluable guidance in the vast field of algebraic geometry by dedicating this paper to his memory.

C. Beltrametti, F. Catanese, C. Ciliberto, A. Lanteri, C. ) © Walter de Gruyter 2002 26 L. 3. 4. K-cohomology and motivic cohomology 5. 1. 2. Srinivas’ example 51 53 55 55 56 0. Introduction Let X be an algebraic C-scheme. The singular cohomology groups H ∗ (X, Z(·)) carry a mixed Hodge structure, see [11, III]. , those having non-zero Hodge numbers in the set {(0, 0), (0, −1), (−1, 0), (−1, −1)}. Therefore, these cohomological invariants of algebraic varieties would be algebraically defined as 1-motives over arbitrary base fields or schemes.

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