Suslin's singular homology and cohomology
Abstract
We discuss Suslin's singular homology and cohomology. In the first half we examine the p-part in characteristic p, and the situation over non-algebraically closed fields. In the second half we focus on finite base fields. We study finite generation properties, and give a modified definition which behaves like a homology theory: in degree zero it is a copy of Z for each connected component, in degree one it is related to the abelianized (tame) fundamental group, even for singular schemes, and it is expected to be finitely generated in general.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2009
- DOI:
- 10.48550/arXiv.0912.1168
- arXiv:
- arXiv:0912.1168
- Bibcode:
- 2009arXiv0912.1168G
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - K-Theory and Homology;
- 14F35;
- 14C25;
- 14F42;
- 19E15