Mishchenko and Quillen formulas for oriented cohomology pretheories

Author:
E. Shinder

Translated by:
B. M. Bekker

Original publication:
Algebra i Analiz, tom **18** (2006), nomer 4.

Journal:
St. Petersburg Math. J. **18** (2007), 671-678

MSC (2000):
Primary 14F43

Published electronically:
May 29, 2007

MathSciNet review:
2262589

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Abstract | References | Similar Articles | Additional Information

Abstract: Two formulas mentioned in the title are generalized to arbitrary oriented cohomology pretheories on algebraic varieties.

**[Har]**Robin Hartshorne,*Algebraic geometry*, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR**0463157****[P1]**I. Panin,*Push-forwards in oriented cohomology theories of algebraic varieties*. II, http://www. math.uiuc.edu/K-theory/0619/2003.**[PS]**I. Panin and A. Smirnov,*Push-forwards in oriented cohomology theories of algebraic varieties*, http://www.math.uiuc.edu/K-theory/0459/2000.**[Pa]**I. Panin,*Riemann-Roch theorems for oriented cohomology*, Axiomatic, enriched and motivic homotopy theory, NATO Sci. Ser. II Math. Phys. Chem., vol. 131, Kluwer Acad. Publ., Dordrecht, 2004, pp. 261–333. MR**2061857**, 10.1007/978-94-007-0948-5_8**[Qu1]**Daniel Quillen,*On the formal group laws of unoriented and complex cobordism theory*, Bull. Amer. Math. Soc.**75**(1969), 1293–1298. MR**0253350**, 10.1090/S0002-9904-1969-12401-8**[N]**S. P. Novikov,*Methods of algebraic topology from the point of view of cobordism theory*, Izv. Akad. Nauk SSSR Ser. Mat.**31**(1967), 855–951 (Russian). MR**0221509**

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Additional Information

**E. Shinder**

Affiliation:
Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ Prospect 28, Staryĭ Peterhof, St. Petersburg 198904, Russia

Email:
shinder@list.ru

DOI:
https://doi.org/10.1090/S1061-0022-07-00966-1

Keywords:
Complex cobordism theory,
oriented cohomology pretheory,
Quillen's formula

Received by editor(s):
February 22, 2006

Published electronically:
May 29, 2007

Article copyright:
© Copyright 2007
American Mathematical Society