Open AccessFrobenius actions on the de Rham cohomology of Drinfeld modules
Author(s) -
Ernst-Ulrich Gekeler
Publication year - 2011
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-2011-05422-x
Subject(s) - algorithm , annotation , artificial intelligence , computer science , mathematics
We study the action of endomorphisms of a Drinfeld A A -module ϕ \phi on its de Rham cohomology H D R ( ϕ , L ) H_{DR}(\phi ,L) and related modules, in the case where ϕ \phi is defined over a field L L of finite A A -characteristic p \frak p . Among others, we find that the nilspace H 0 H_0 of the total Frobenius F r D R Fr_{DR} on H D R ( ϕ , L ) H_{DR}(\phi ,L) has dimension h = h = height of ϕ \phi . We define and study a pairing between the p \frak p -torsion p ϕ _{\frak p}\phi of ϕ \phi and H D R ( ϕ , L ) H_{DR}(\phi ,L) , which becomes perfect after dividing out H 0 H_0 .