Rad HAZU, Matematičke znanosti, Vol. 21 (2017), 53-74.

SOME EXTENSIONS OF THE NOTION OF LOOP GRASSMANNIANS

Ivan Mirković

Abstract.   We report an ongoing attempt to establish in algebraic geometry certain analogues of topological ideas, The main goal is to associate to a scheme X over a commutative ring k its “relative motivic homology” which is again an algebro geometric object over the base k. This is motivated by Number Theory, so the Poincaré duality for this relative motivic homology should be an algebro geometric incarnation of Class Field Theory.

2010 Mathematics Subject Classification.   11S37, 14F42.

Key words and phrases.   Loop Grassmannian, class field theory, motivic homology.

DOI: https://doi.org/10.21857/yvjrdcnqpy

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