## The Reich trace formula. Appendice: Une base normale pour l’algèbre de Banach de Reich by Jean Fresnel.(English)Zbl 0561.12013

Cohomologie p-adique, Astérisque 119/120, 129-150 (1984).
[For the entire collection see Zbl 0542.00006.]
The Dwork-Reich trace formula has been established for hypersurfaces given by the homogeneous polynomial g such that the reduction $$\bar g$$ of g satisfies a certain condition. According to the Monsky-Washnitzer cohomology this condition on $$\bar g$$ is superfluous. In the present paper Reich’s elementary proof is examined. Using results on orthogonal bases, provided in an appendix by J. Fresnel, the proof of Reich is given avoiding this condition on g. The result on bases is the following: a certain family of affinoid algebras $$F_{\epsilon,\Delta,g}$$ has a simultaneous orthogonal basis. For the convenience of the reader a selfcontained proof is presented.
Reviewer: M.van der Put

### MSC:

 12J27 Krasner-Tate algebras 14G20 Local ground fields in algebraic geometry 14F30 $$p$$-adic cohomology, crystalline cohomology

Zbl 0542.00006