A remark on the HochschildKostantRosenberg theorem in characteristic p
Abstract
We prove a HochschildKostantRosenberg decomposition theorem for smooth proper schemes $X$ in characteristic $p$ when $\dim X\leq p$. The best known previous result of this kind, due to Yekutieli, required $\dim X<p$. Yekutieli's result follows from the observation that the denominators appearing in the classical proof of HKR do not divide $p$ when $\dim X<p$. Our extension to $\dim X=p$ requires a homological fact: the Hochschild homology of a smooth proper scheme is selfdual.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 DOI:
 10.48550/arXiv.1710.06039
 arXiv:
 arXiv:1710.06039
 Bibcode:
 2017arXiv171006039A
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology