Preprints

The following articles are under way:

  • Arakelov motivic cohomology I (joint with Jakob Scholbach, in preparation). The main results here are stable A1-representability of Deligne cohomology, a new construction of the Beilinson regulator and the height pairing, construction of so called Arakelov motivic cohomology groups for arithmetic schemes, with applications to formulations of conjectures on zeta values (by Beilinson, Soule, Lichtenbaum, Scholbach, Flach, and others).
  • Products on Arakelov motivic cohomology (in preparation, joint with Peter Arndt)
  • Arakelov motivic cohomology II (joint with Scholbach, in preparation)
  • A note on A1-representability of Bloch-Ogus theories (in preparation)
  • Gluing of cohomology theories for arithmetic schemes (in preparation)

The following projects are things I am thinking about which will appear at some point but not in the immediate future:

  • Rough guide to cohomology theories in arithmetic geometry
  • First steps towards higher arithmetic Riemann-Roch
  • Arakelov motivic cohomology III. The aim of this project is to integrate Arakelov motivic cohomology with the Weil-etale topology, following ideas of Matthias Flach.

Author: admin
Date: Saturday, 12. December 2009 3:12
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