Back to Search
Start Over
Positive characteristic Poincar\'e Lemma
- Publication Year :
- 2021
-
Abstract
- Let $K$ be a field of characteristic $ p>0$ and $\omega$ be an $r$-form in $ K^n$. In this case, differently of fields of characteristic zero, the Poincar\'e Lemma is not true because there are closed $ r$-forms that are not exact. We present here a definition of a $p$-closed $r$-forms and a version of the Poincar\'e Lemma that is valid for $p$-closed polynomial or rational $r$-forms on $ K^n$ and, as a consequence, the de Rham cohomology modules of $ K^n$ are not trivial.
- Subjects :
- Mathematics - Rings and Algebras
13N15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2110.08888
- Document Type :
- Working Paper