Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



Frobenius actions on the de Rham cohomology of Drinfeld modules

Author: Ernst-Ulrich Gekeler
Journal: Trans. Amer. Math. Soc. 363 (2011), 3167-3183
MSC (2010): Primary 11G09; Secondary 11R58
Published electronically: January 27, 2011
MathSciNet review: 2775802
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the action of endomorphisms of a Drinfeld $ A$-module $ \phi$ on its de Rham cohomology $ H_{DR}(\phi,L)$ and related modules, in the case where $ \phi$ is defined over a field $ L$ of finite $ A$-characteristic $ \frak p$. Among others, we find that the nilspace $ H_0$ of the total Frobenius $ Fr_{DR}$ on $ H_{DR}(\phi,L)$ has dimension $ h = $ height of $ \phi$. We define and study a pairing between the $ \frak p$-torsion $ _{\frak p}\phi$ of $ \phi$ and $ H_{DR}(\phi,L)$, which becomes perfect after dividing out $ H_0$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 11G09, 11R58

Retrieve articles in all journals with MSC (2010): 11G09, 11R58

Additional Information

Ernst-Ulrich Gekeler
Affiliation: FR 6.1 Mathematik, E2 4, Universität des Saarlandes, Postfach 15 11 50, D-66041 Saarbrücken, Germany

Keywords: Drinfeld module, de Rham cohomology
Received by editor(s): July 20, 2009
Published electronically: January 27, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia