A Weil-Barsotti formula for Drinfeld modules

Abstract

We study the group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t-module. Our main result is a Drinfeld module analogue of the Weil-Barsotti formula for abelian varieties. Extensions of general t-modules are also considered, in particular extensions of tensor powers of the Carlitz module. We motivate these results from various directions and compare to the situation of elliptic curves.

20 pages, latex file. To appear in Journal of Number Theory

References in corpus (2)

• Real Multiplication and noncommutative geometry
• Linear independence of Gamma values in positive characteristic

Cited by in corpus (10)

• The de Rham isomorphism for Drinfeld modules over Tate algebras
• Hyperderivatives of periods and quasi-periods for Anderson $t$-modules
• Shtuka cohomology and special values of Goss L-functions
• The Carlitz shtuka
• Extensions of CM elliptic curves and orbit counting on the projective line
• Linear relations among double zeta values in positive characteristic
• Periods of third kind for rank 2 Drinfeld modules and algebraic independence of logarithms
• On lower bounds of the dimensions of multizeta values in positive characteristic
• Analytic continuation of Kochubei multiple polylogarithms and its applications
• Extensions of abelian varieties defined over a number field