The Exact Poincaré Lemma in Crystalline Cohomology of Higher Level

✍ Scribed by Bernard Le Stum; Adolfo Quirós

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 224 KB
• Volume: 240
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.8749

✦ Synopsis

We prove a formal Poincare Lemma in crystalline cohomology of higher level ánd we derive a de Rham interpretation of crystalline cohomology of higher level. We also define the Spencer complex of higher level and show that it can be used to compute the cohomology of arithmetic D D-modules. ᮊ 2001 Academic Press CONTENTS 1. The de Rham complex.

2. Integration of differential forms of higher le¨el.

3. The Formal Poincare Lemma in higher le¨el.

The Poincare Lemma in crystalline cohomology.

Complements and applications.