scholarly journals Kolyvagin’s method for Chow groups of Kuga–Sato varieties over ring class fields

2015 ◽  
Vol 39 (2) ◽  
pp. 147-167 ◽  
Author(s):  
Yara Elias
Keyword(s):  
Chow Groups ◽  
Class Fields

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

2017 ◽  
Author(s):  
Claire Voisin
Keyword(s):  
Recent Work ◽  
Chow Groups ◽  
Ring Structure ◽  
Complete Intersections ◽  
Algebraic Varieties ◽  
Chow Ring ◽  
Hodge Structures ◽  
Chow Rings ◽  
Geometric Methods ◽  
The Right

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The book is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by the author. It focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by the author looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

scholarly journals On the first Steenrod square for Chow groups

2013 ◽  
Vol 135 (1) ◽  
pp. 53-63 ◽  
Author(s):  
Olivier Haution
Keyword(s):  
Chow Groups ◽  
Steenrod Square

scholarly journals Existence of Generalized Local Class Fields

1953 ◽  
Vol 39 (10) ◽  
pp. 1100-1103 ◽  
Author(s):  
G. Whaples
Keyword(s):  
Class Fields

scholarly journals On the Computation of Hilbert Class Fields

1998 ◽  
Vol 69 (2) ◽  
pp. 213-230 ◽  
Author(s):  
M. Daberkow ◽  
M. Pohst
Keyword(s):  
Class Fields

Klein Units in Arbitrary Class Fields

1981 ◽  
pp. 269-310
Author(s):  
Daniel S. Kubert ◽  
Serge Lang
Keyword(s):  
Class Fields

Chow groups of some generically twisted flag varieties

2017 ◽  
Vol 2 (2) ◽  
pp. 341-356 ◽  
Author(s):  
Nikita Karpenko
Keyword(s):  
Chow Groups ◽  
Flag Varieties
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