# The Legendre determinant form for Drinfeld modules in arbitrary rank

1 CTN - Combinatoire, théorie des nombres
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : For each positive integer $r$, we construct a nowhere-vanishing, single-cuspidal Drinfeld modular form for $\GL_r(\FF_q[\theta])$, necessarily of least possible weight, via determinants using rigid analytic trivializations of the universal Drinfeld module of rank $r$ and deformations of vectorial Eisenstein series. Along the way, we deduce that the cycle class map from de Rham cohomology to Betti cohomology is an isomorphism for Drinfeld modules of all ranks over $\FF_q[\theta]$.
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Preprints, Working Papers, ...

Cited literature [17 references]

https://hal.archives-ouvertes.fr/hal-01067333
Contributor : Rudolph Perkins <>
Submitted on : Tuesday, September 23, 2014 - 1:42:36 PM
Last modification on : Friday, March 8, 2019 - 9:38:03 AM
Document(s) archivé(s) le : Wednesday, December 24, 2014 - 8:55:18 PM

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### Identifiers

• HAL Id : hal-01067333, version 1
• ARXIV : 1409.6693

### Citation

Rudolph Perkins. The Legendre determinant form for Drinfeld modules in arbitrary rank. 2014. ⟨hal-01067333⟩

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