Algebraic Cycles and Special Horikawa Surfaces

Algebraic cycles on a very special EPW sextic

Motivated by the Beauville–Voisin conjecture about Chow rings of powers of K3 surfaces, we consider a similar conjecture for Chow rings of powers of EPW sextics. We prove part of this conjecture for the very special EPW sextic studied by Donten–Bury et alii. We also prove some other results concerning the Chow groups of this very special EPW sextic, and of certain related hyperkähler fourfolds....

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...

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...

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