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

 

Riemann-Roch theorem for operations in cohomology of algebraic varieties


Author: A. L. Smirnov
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 18 (2006), nomer 5.
Journal: St. Petersburg Math. J. 18 (2007), 837-856
MSC (2000): Primary 14F25, 14F42, 14F43, 14F99
Published electronically: August 10, 2007
MathSciNet review: 2301046
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Abstract | References | Similar Articles | Additional Information

Abstract: The Riemann-Roch theorem for multiplicative operations in oriented cohomology theories for algebraic varieties is proved and an explicit formula for the corresponding Todd classes is given. The formula obtained can also be applied in the topological situation, and the theorem can be regarded as a change-of-variables formula for the integration of cohomology classes.


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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/S1061-0022-07-00976-4
PII: S 1061-0022(07)00976-4
Keywords: Algebraic variety, oriented cohomology theory, transfer, characteristic class, Todd class, Riemann--Roch theorem
Received by editor(s): May 29, 2006
Published electronically: August 10, 2007
Additional Notes: Supported by RFBR (grant 06-01-00741)
Article copyright: © Copyright 2007 American Mathematical Society