Algebraic cycles and the classical groups II: Quaternionic cycles

Quaternionic Algebraic Cycles and Reality

In this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real Brauer-Severi varieties, under the action of the Galois group Gal(C/R). Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymour’s quaternionic K-theory, and the other one classifies and equivariant cohomology theory Z∗(−) which is a natural recip...

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 and Motivic Iterated Integrals Ii

This is a sequel to [FJ]. It will give a more natural framework for constructing elements in the Hopf algebra χF of framed mixed Tate motives according to Bloch and Křiž [BK]. This framework allows us to extend the results of [FJ] to interpret all multiple zeta values (including the divergent ones) and the multiple polylogarithms in one variable as elements of χF . It implies that the pro-unipo...

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...