Morphic cohomology

General Introduction
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Search results
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Online References
Friedlander on BlochOgus properties
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Paper References
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Definition
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Properties
The BlochOgus axioms are satisfied for morphic cohomology/Lawson homology. See Friedlander: BlochOgus 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 AbdÃ³ RoigMaranges 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
Techniques, Computations, and Conjectures for SemiTopological Ktheory, by Eric M. Friedlander, Christian Haesemeyer, and Mark E. Walker: K0621
The morphic AbelJacobi map, by Mark E. Walker
arXiv:1008.3685 Equivariant Semitopological Invariants, Atiyah's KRtheory, and Real Algebraic Cycles from arXiv Front: math.AG by Jeremiah Heller, Mircea Voineagu We establish an AtiyahHirzebruch type spectral sequence relating real morphic cohomology and real semitopological Ktheory and prove it to be compatible with the AtiyahHirzebruch spectral sequence relating Bredon cohomology and Atiyah's KRtheory 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 semitopological Ktheory of some real varieties. As another application of this spectral sequence we give an alternate proof of the LichtenbaumQuillen conjecture over $\R$, extending an earlier proof of Karoubi and Weibel.
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Other Information
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