Algebraic cycles and the classical groups. I: real cycles

Algebraic Cycles and the Classical

Algebraic Cycles and Additive Chow Groups

A report on recent results and outstanding problems concerning additive chow groups. “Mighty oaks from little acorns grow.”

Algebraic Cycles

This article is based on a talk given by V. Srinivas at the MRI, Allahabad. We give an account of the theory of algebraic cycles where the stress is not on the spate of conjectures (Hodge, Tate, Grothendieck, Bloch-Beilinson, etc.) that define the picture of this theory today, but rather on the key examples that refined and delineated this picture. Some of the deepest aspects of the theory of a...

Cycles in Algebraic Systems

2. Cycles and their terminology. Let L be an n Xn Latin square or, alternatively, let Q be a quasigroup of order n. Let M be the set of n2 ordered triplets ijk, where k is the entry in the ith row and jth column of L. If 5 is the set of n2 ordered pairs ij, and if 7r,:Af—>S is the projection parallel to the ith coordinate (for example, ir2(ijk) = ik), then for each i, l^i^3, t< is onto S (or eq...

Algebraic Cycles and Connes Periodicity

We apply the classical technique on cyclic objects of Alain Connes to various objects, in particular to the higher Chow complex of S. Bloch to prove a Connes periodicity long exact sequence involving motivic cohomology groups. The Cyclic higher Chow groups and the Connes higher Chow groups of a variety are defined in the process and various properties of them are deduced from the known properti...