Posted on

A survey of the Hodge conjecture by James D. Lewis

By James D. Lewis

This ebook offers an creation to a subject of significant curiosity in transcendental algebraic geometry: the Hodge conjecture. along with 15 lectures plus addenda and appendices, the quantity is predicated on a sequence of lectures introduced through Professor Lewis on the Centre de Recherches Mathematiques (CRM). The publication is a self-contained presentation, thoroughly dedicated to the Hodge conjecture and similar subject matters. It comprises many examples, and so much effects are thoroughly confirmed or sketched. the incentive at the back of some of the effects and history fabric is supplied. This complete method of the publication supplies it a ``user-friendly'' variety. Readers needn't seek somewhere else for numerous effects. The ebook is appropriate to be used as a textual content for a subject matters direction in algebraic geometry; comprises an appendix via B. Brent Gordon.

Show description

Read Online or Download A survey of the Hodge conjecture PDF

Best algebraic geometry books

Configuration spaces over Hilbert schemes and applications

The most topics of this ebook are to set up the triple formulation with none hypotheses at the genericity of the morphism, and to increase a idea of entire quadruple issues, that's a primary step in the direction of proving the quadruple element formulation lower than much less restrictive hypotheses. This publication might be of curiosity to graduate scholars and researchers within the box of algebraic geometry.

Understanding Geometric Algebra for Electromagnetic Theory

This booklet goals to disseminate geometric algebra as a simple mathematical software set for operating with and realizing classical electromagnetic idea. it is objective readership is a person who has a few wisdom of electromagnetic thought, predominantly usual scientists and engineers who use it during their paintings, or postgraduate scholars and senior undergraduates who're looking to develop their wisdom and raise their knowing of the topic.

An Excursion in Diagrammatic Algebra: Turning a Sphere from Red to Blue

The purpose of this e-book is to provide as distinctive an outline as is feasible of 1 of the main attractive and complex examples in low-dimensional topology. this instance is a gateway to a brand new proposal of upper dimensional algebra during which diagrams exchange algebraic expressions and relationships among diagrams characterize algebraic kin.

Algebraic Geometry, Hirzebruch 70: Proceedings of an Algebraic Geometry Conference in Honor of F. Hirzebruch's 70th Birthday, May 11-16, 1998, Stefan ... Mathematical

This ebook provides the court cases from the convention on algebraic geometry in honor of Professor Friedrich Hirzebruch's seventieth Birthday. the development used to be held on the Stefan Banach foreign Mathematical heart in Warsaw (Poland). the subjects lined within the booklet contain intersection concept, singularities, low-dimensional manifolds, moduli areas, quantity thought, and interactions among mathematical physics and geometry.

Additional resources for A survey of the Hodge conjecture

Sample text

Pour N > 4, Coker η 4 s’injecte dans CH3 (X)tors . 4 ([20, 22, 23]). Pour toute quadrique X, le groupe CH3 (X)tors est d’ordre 1 ou 2. De plus, on a CH3 (X)tors = 0 pour N > 10. En particulier (cf. 5. Coker η 4 = 0 pour N > 10 et Coker η24 = 0 pour N > 14. 3 est N = 4. 2) : a) Voisine : d = 1, XE hyperbolique. b) Interm´ediaire : d = 1, XE isotrope, non hyperbolique. c) Albert : d = 1. d) Albert virtuelle : d = 1, XE anisotrope. 6 ([18]). Soit φ une forme quadratique d´efinissant X (avec dim X = 4).

Voevodsky, V. : Triangulated categories of motives over a field. In Cycles, transfers and motivic cohomology theories, Annals of Math. Studies 143, 2000 ` paraˆıtre aux Publ. 45. Voevodsky, V. : Motivic cohomology with Z/2 coefficients. A ´ Math. IHES. 46. Voevodsky, V. : Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic. Int. Math. Res. Notices 2002, 351–355 47. Wang, S. : On the commutator group of a simple algebra. Amer. J. Math. ru Introduction This text is the notes of my lectures at the mini-course “M´ethodes g´eom´etriques en th´eorie des formes quadratiques” at the Universit´e d’Artois, Lens, June 26–28, 2000.

71 76 92 98 References . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 1 Grothendieck Category of Chow Motives Let k be any field, and SmProj(k) the category of smooth projective varieties over k. We define the category of correspondences C (k) in the following way: the set Ob C (k) is identified with the set Ob SmProj(k) (the object corresponding to X will be denoted by [X]), and if X = i Xi is the decomposition into a disjoint union of connected components, then CHdim Xi (Xi × Y ), HomC (k) ([X], [Y ]) := i where CHdim Xi (Xi × Y ) is the Chow group of dim Xi -dimensional cycles on Xi × Y .

Download PDF sample

Rated 4.96 of 5 – based on 47 votes