By Eduardo Cattani,Fouad El Zein,Phillip A. Griffiths,Lê Dũng Tráng
This booklet presents a entire and updated advent to Hodge theory—one of the important and so much vivid parts of up to date mathematics—from top experts at the topic. the themes diversity from the elemental topology of algebraic forms to the research of adaptations of combined Hodge constitution and the Hodge thought of maps. Of specific curiosity is the examine of algebraic cycles, together with the Hodge and Bloch-Beilinson Conjectures. in response to lectures added on the 2010 summer time university on Hodge thought on the ICTP in Trieste, Italy, the ebook is meant for a wide team of scholars and researchers. The exposition is as available as attainable and does not require a deep heritage. while, the ebook offers a few subject matters on the vanguard of present research.
The booklet is split among introductory and complex lectures. The introductory lectures tackle Kähler manifolds, adaptations of Hodge constitution, combined Hodge constructions, the Hodge concept of maps, interval domain names and interval mappings, algebraic cycles (up to and together with the Bloch-Beilinson conjecture) and Chow teams, sheaf cohomology, and a brand new therapy of Grothendieck’s algebraic de Rham theorem. The complex lectures tackle a Hodge-theoretic standpoint on Shimura forms, the unfold philosophy within the research of algebraic cycles, absolute Hodge sessions (including a brand new, self-contained facts of Deligne’s theorem on absolute Hodge cycles), and edition of combined Hodge structures.
The individuals contain Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. eco-friendly, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.