Search results for "Algebraic cycle"
showing 2 items of 12 documents
Applications to Algebraic Cycles: Nori's Theorem
2017
Deligne cohomology is a tool that makes it possible to unify the study of cycles through an object that classifies extensions of ( p , p )-cycles by points in the p -th intermediate Jacobian (which is the target of the Abel–Jacobi map on cycles of codimension p ). This is treated in Section 10.1 with applications to normal functions. Before giving the proof of Nori's theorem in Section 10.6, we need some results from mixed Hodge theory. These are proven in Section 10.2 where we also state different variants of the theorem. Sections 10.3 and 10.4 treat a localto- global principle and an extension of the method of Jacobian representations of cohomology which are both essential for the proof. …
General Theory: Algebraic Point of View
2009
It is convenient to divide our study of pip-spaces into two stages. In the first one, we consider only the algebraic aspects. That is, we explore the structure generated by a linear compatibility relation on a vector space V , as introduced in Section I.2, without any other ingredient. This will lead us to another equivalent formulation, in terms of particular coverings of V by families of subspaces. This first approach, purely algebraic, is the subject matter of the present chapter. Then, in a second stage, we introduce topologies on the so-called assaying subspaces \(\{V_r \}\). Indeed, as already mentioned in Section I.2, assuming the partial inner product to be nondegenerate implies tha…