English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Differential characters of Drinfeld modules and de Rham cohomology

MPS-Authors
/persons/resource/persons240833

Saha,  Arnab
Max Planck Institute for Mathematics, Max Planck Society;

Locator
Fulltext (public)

arXiv:1703.05677.pdf
(Preprint), 449KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Borger, J., & Saha, A. (2019). Differential characters of Drinfeld modules and de Rham cohomology. Algebra & Number Theory, 13(4), 797-837. doi:10.2140/ant.2019.13.797.


Cite as: http://hdl.handle.net/21.11116/0000-0004-9942-5
Abstract
We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differential characters of elliptic curves in differential algebra, both of which have had notable Diophantine applications. We determine the structure of the group of differential characters. This shows the existence of a family of interesting differential modular functions on the moduli of Drinfeld modules. It also leads to a canonical $F$-crystal equipped with a map to the de Rham cohomology of the Drinfeld module. This $F$-crystal is of a differential-algebraic nature, and the relation to the classical cohomological realizations is presently not clear.