Morphic cohomology

• General Introduction

  See also Topological cycle cohomology, Lawson homology, Bloch-Ogus cohomology

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• Search results

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• Online References

  Friedlander on Bloch-Ogus properties

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• Paper References

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• Definition

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• Properties

  The Bloch-Ogus axioms are satisfied for morphic cohomology/Lawson homology. See Friedlander: Bloch-Ogus properties for topological cycle theory

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• Standard theorems

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• Open Problems

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• Connections to Number Theory

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• Computations and Examples

  arXiv:1001.3106 Morphic cohomology of toric varieties from arXiv Front: math.AG by Abdó Roig-Maranges In this paper we construct a spectral sequence computing a modified version of morphic cohomology of a toric variety (even when it is singular) in terms of combinatorial data coming from the fan of the toric variety.

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• History and Applications

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• Some Research Articles

  Friedlander and Walker

  Techniques, Computations, and Conjectures for Semi-Topological K-theory, by Eric M. Friedlander, Christian Haesemeyer, and Mark E. Walker: K0621

  The morphic Abel-Jacobi map, by Mark E. Walker

  arXiv:1008.3685 Equivariant Semi-topological Invariants, Atiyah's KR-theory, and Real Algebraic Cycles from arXiv Front: math.AG by Jeremiah Heller, Mircea Voineagu We establish an Atiyah-Hirzebruch type spectral sequence relating real morphic cohomology and real semi-topological K-theory and prove it to be compatible with the Atiyah-Hirzebruch spectral sequence relating Bredon cohomology and Atiyah's KR-theory constructed by Dugger. An equivariant and a real version of Suslin's conjecture on morphic cohomology are formulated, proved to come from the complex version of Suslin conjecture and verified for certain real varieties. In conjunction with the spectral sequences constructed here this allows the computation of the real semi-topological K-theory of some real varieties. As another application of this spectral sequence we give an alternate proof of the Lichtenbaum-Quillen conjecture over $\R$, extending an earlier proof of Karoubi and Weibel.

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• Other Information

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• Comments Posted

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• General Introduction
• Search results
• Online References
• Paper References
• Definition
• Properties
• Standard theorems
• Open Problems
• Connections to Number Theory
• Computations and Examples
• History and Applications
• Some Research Articles
• Other Information
• Comments Posted
• Comments