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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Orientations and transfers in cohomology of algebraic varieties
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by A. L. Smirnov
Translated by: B. M. Bekker
St. Petersburg Math. J. 18 (2007), 305-346
DOI: https://doi.org/10.1090/S1061-0022-07-00952-1
Published electronically: March 20, 2007
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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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Bibliographic 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
  • Received by editor(s): January 10, 2006
  • Published electronically: March 20, 2007
  • Additional Notes: Partially supported by RFBR (grant no. 03-01-00633a)
  • © Copyright 2007 American Mathematical Society
  • Journal: St. Petersburg Math. J. 18 (2007), 305-346
  • MSC (2000): Primary 14F99
  • DOI: https://doi.org/10.1090/S1061-0022-07-00952-1
  • MathSciNet review: 2244939