Arithmetic normal functions and filtrations on Chow groups

Author:
James D. Lewis

Journal:
Proc. Amer. Math. Soc. **140** (2012), 2663-2670

MSC (2010):
Primary 14C25; Secondary 14C30, 14C35

DOI:
https://doi.org/10.1090/S0002-9939-2011-11130-4

Published electronically:
December 27, 2011

MathSciNet review:
2910754

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a smooth projective variety, and let be the higher Chow group defined by Bloch. Saito and Asakura defined a descending candidate Bloch-Beilinson filtration , using the language of mixed Hodge modules. Another more geometrically defined filtration is constructed by Kerr and Lewis in terms of germs of normal functions. We show that under the assumptions (i) where is defined over , and (ii) the general Hodge conjecture, that coincides with the aforementioned geometric filtration. More specifically, it is characterized in terms of germs of reduced arithmetic normal functions.

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Additional Information

**James D. Lewis**

Affiliation:
Department of Mathematical and Statistical Sciences, 632 Central Academic Building, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Email:
lewisjd@ualberta.ca

DOI:
https://doi.org/10.1090/S0002-9939-2011-11130-4

Keywords:
Bloch-Beilinson filtration,
arithmetic normal function,
Chow group

Received by editor(s):
March 28, 2010

Received by editor(s) in revised form:
March 16, 2011

Published electronically:
December 27, 2011

Additional Notes:
The author was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.

Communicated by:
Lev Borisov

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.