The Legendre determinant form for Drinfeld modules in arbitrary rank

Rudolph Perkins (1)

1 CTN - Combinatoire, théorie des nombres

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 $\FF_q[\theta]$.

Mots clés: Drinfeld modular forms; deformations; cohomology; $t$-motives; Legendre period relation

Domaines: Théorie des nombres [math.NT]

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