T-spectra and Poincaré duality

Panin, Ivan; Yagunov, Serge

doi:10.1515/crelle.2008.030

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Introduction2

2]) the Homomorphism A(t T − S) → A(t ) Is Just The Pull-1

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Cited by 2 publications

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“…Finally one should stress that a version of the Poincaré duality isomorphism between a cohomology and a homology theory represented by an oriented T -spectrum is proved in [32]. It is shown there that trace operators in cohomology coincide with the expected ones.…”

Section: 2]) the Homomorphism A(t T − S) → A(t ) Is Just The Pull-mentioning

confidence: 97%

Oriented cohomology theories of algebraic varieties II

Panin

2009

Homology, Homotopy and Applications

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The concept of oriented cohomology theory is well-known in topology. Examples of these kinds of theories are complex cobordism, complex K-theory, usual singular cohomology, and Morava K-theories. A specific feature of these cohomology theories is the existence of trace operators (or Thom-Gysin operators, or push-forwards) for morphisms of compact complex manifolds. The main aim of the present article is to develop an algebraic version of the concept. Bijective correspondences between orientations, Chern structures, Thom structures and trace structures on a given ring cohomology theory are constructed. The theory is illustrated by singular cohomology, motivic cohomology, algebraic K-theory, the algebraic cobordism of Voevodsky and by other examples.

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Section: 2]) the Homomorphism A(t T − S) → A(t ) Is Just The Pull-mentioning

confidence: 97%

Oriented cohomology theories of algebraic varieties II

Panin

2009

Homology, Homotopy and Applications

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“…Essentially, we extend the main statement of [8] to this category. Many known results can easily be interpreted in these terms.…”

Section: Introductionmentioning

confidence: 94%

“…In particular, we get a generalization of the Friedlander-Voevodsky duality theorem [4] to the case of the ground field of arbitrary characteristic. The proof of this fact, involving the main result of [8], was kindly conveyed to the authors by Andreǐ Suslin in a private communication.…”

Section: Introductionmentioning

confidence: 99%