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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

Orientations and transfers in cohomology of algebraic varieties


Author: A. L. Smirnov
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 18 (2006), nomer 2.
Journal: St. Petersburg Math. J. 18 (2007), 305-346
MSC (2000): Primary 14F99
Published electronically: March 20, 2007
MathSciNet review: 2244939
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Abstract | References | Similar Articles | Additional Information

Abstract: Algebro-geometric cohomology theories are described axiomatically, with a systematic treatment of their orientations. For every oriented theory, transfer mappings are constructed for mappings of smooth varieties that are proper on supports. In some basic cases, transfers are calculated. The presentation is illustrated by motivic cohomology, $ K$-theory, algebraic cobordism, and other examples.


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Additional Information

A. L. Smirnov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: smirnov@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-07-00952-1
PII: S 1061-0022(07)00952-1
Keywords: Algebraic variety, motivic cohomology, algebraic cobordism, orientation, transfer, characteristic class, residue
Received by editor(s): January 10, 2006
Published electronically: March 20, 2007
Additional Notes: Partially supported by RFBR (grant no. 03-01-00633a)
Article copyright: © Copyright 2007 American Mathematical Society