Vol. 7, No. 2, 2022

Download this article
Download this article For screen
For printing
Recent Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Unramified cohomology, integral coniveau filtration and Griffiths groups

Shouhei Ma

Vol. 7 (2022), No. 2, 223–236

We prove that the degree k unramified cohomology Hnr k(X, ) of a smooth complex projective variety X with small CH 0(X) has a filtration of length [k2], whose first piece is the torsion part of the quotient of Hk+1(X, ) by its coniveau 2 subgroup, and whose next graded piece is controlled by the Griffiths group Griff k2+1(X) when k is even and is related to the higher Chow group CH (k+3)2(X,1) when k is odd. The first piece is a generalization of the Artin–Mumford invariant (k = 2) and the Colliot-Thélène–Voisin invariant (k = 3). We also give an analogous result for the -cohomology Hdk(X,d()), d = dim X.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

unramified cohomology, integral coniveau filtration, Griffiths group, $\mathcal H$-cohomology, birational invariant
Mathematical Subject Classification
Primary: 14C15, 14C25, 14F43
Received: 12 October 2020
Revised: 23 December 2021
Accepted: 12 January 2022
Published: 13 September 2022
Shouhei Ma
Department of Mathematics
Tokyo Institute of Technology