Holmstrom Morphic cohomology

Morphic cohomology

Friedlander on Bloch-Ogus properties

---

Morphic cohomology

http://www.math.uiuc.edu/K-theory/0379: “Holomorphic K-theory sits between algebraic K-theory and topological K-theory in the same way that morphic cohomology sits between motivic cohomology and ordinary cohomology.”

---

Morphic cohomology

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

---

Morphic cohomology

http://www.math.uiuc.edu/K-theory/0379 “With this we define, for any projective variety X, a Chern character map $ch : K^{-i}_{hol}(X) \to \prod_* L^*H^{2*-i}(X)\otimes Q$ from the holomorphic K-theory of X to its morphic cohomology”

Walker on the morphic Abel-Jacobi map

---

Morphic cohomology

MathSciNet

Google Scholar

Google

arXiv: Experimental full text search

arXiv: Abstract search

---

Morphic cohomology

AG (Algebraic geometry)

---

Morphic cohomology

Mixed

---

Morphic cohomology

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

---

Morphic cohomology

Friedlander and Walker

Techniques, Computations, and Conjectures for Semi-Topological K-theory, by Eric M. Friedlander, Christian Haesemeyer, and Mark E. Walker: http://www.math.uiuc.edu/K-theory/0621

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.

---

Morphic cohomology

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.

nLab page on Morphic cohomology