School of Mathematics. This paper is based on the mini-course of five lectures by Claire Voisin, one . 4 Algebraic geometry: classical approach. The Grothendieck ring K 0 ( Var C) of complex algebraic varieties is defined as the quotient of the free abelian group generated by the isomorphism classes [ X] of complex algebraic varieties modulo the relations [ X] = [ Y] + [ X ∖ Y] for all closed subvarieties Y ⊂ X. A CNRS researcher for around thirty years, she now holds the chair in Algebraic Geometry at the Collège de France. Translated from the French by Leila Schneps. His corrected form of the Hodge conjecture is: . Key figures - Math in France Wednesday 9 May At 15:30 Polo Ferrari 1, via Sommarive 5, Povo - Aula Tognoli (room A103) Pure Math., vol. Claire Voisin. 71493517 - Viaf - Claire Voisin, 2008 CNRS and IHES - Yves Benoist, 2011 CNRS and Orsay. Nous remercions GQ de nous permettre d'en présenter aujourd'hui une nouvelle version. I would not say it is essential to read the entire EGA, but since it is the standard reference, it is at least worth getting to know it. Hodge theory in nLab Grothendieck-Lefschetz for ample subvarieties Authors. If X is a smooth variety over the complex numbers, you can use the topological Euler characteristic of the support X ( C) of the scheme. Henri Poincaré Prizes. K3 surfaces and their higher-dimensional generalizations provided by compact hyperkälhler manifolds are a perfect testing ground for central conjectures in algebraic geometry, like the Hodge conjecture, the Tate conjecture, Grothendieck's standard conjectures, Bloch-Beilinson conjectures, etc.. Constructions and Obstructions in Birational Geometry But as legitimate as it is, the question is difficult to answer, because of the particularly abstruse nature of his mathematics and the wealth of notions he . In the appendix Claire Voisin proves a similar result in a different setting using the Chow decomposition of diagonal and unramified cohomology. Ravi Vakil's course notes on Intersection Theory, free on the web, cover a similar selection of topics from Fulton. 16. PDF ScIENcES Le Putéolien Michel Talagrand, prix Shaw 2019 en mathématiques Presented by Claire Voisin. Pseudoeffective and nef classes on abelian varieties - Cambridge 5 Complex manifolds. Claire Voisin, On integral Hodge classes on uniruled or Calabi-Yau threefolds, Moduli spaces and arithmetic geometry, Adv. Famous for her original and multifarious research, she won numerous rewards and has achieved exceptional international credit. Derived categories and Chow groups of hyperkaehler and Calabi-Yau ... This distinction came as recognition for her major contributions to Complex Algebraic Geometry. 416 Claire Voisin In the papers [6], [10], [8], some constructions are given, which realize geomet-rically for K3-surfaces with large Picard number the Kuga-Satake construction, .