Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Project B5

## Algebraic geometry, cohomology and abelian varieties

Principal Investigator(s) Other Investigators

## Summary:

We study p-adic cohomology theories of algebraic varieties in characteristic p > 0 and their applications. We will further develop the theory of the de Rham-Witt complex and its variant for rigid cohomology. In particular we are interested in the display structure on the cohomology. As in the case of p-divisible groups the displays should form a bridge to p-adic étale cohomology. We will continue to study the implications of the theory of displays for abelian varieties and p-divisible groups.

This project continues the successful work of the project Crystalline cohomology and Abelian manifolds under the direction of and Thomas Zink.

## Recent Preprints:

 12059 Extensions of group schemes of $\mu$-type by a constant group scheme PDF | PS.GZ 12058 Étale subquotients of prime torsion of abelian schemes PDF | PS.GZ 12057 Modularity of abelian varieties over Q with bad reduction in one prime only PDF | PS.GZ 08090 Infinitesimal deformation of ultrametric differential equations PDF | PS.GZ 08067 Breuil's classification of p-divisible groups over regular local rings of arbitrary dimension PDF | PS.GZ 08066 Overconvergent de Rham-Witt Cohomology PDF | PS.GZ 08065 Overconvergent Witt Vectors PDF | PS.GZ 08007 Arithmetic and Differential Swan conductors of rank one representations with finite local monodromy. PDF | PS.GZ 07015 Del Pezzo surfaces of degree 1 and jacobians PDF | PS.GZ 06062 p-Adic Confluence of q-Difference Equations PDF | PS.GZ