TL;DR
This paper introduces and investigates Drinfeld-Stuhler modules, exploring their algebraic properties, endomorphism rings, and fields of moduli, extending the theory of Drinfeld modules with new structures and classifications.
Contribution
It provides foundational results on Drinfeld-Stuhler modules, including their endomorphism rings and existence of modules with large endomorphism algebras, analogous to CM and supersingular cases.
Findings
Basic properties of Drinfeld-Stuhler modules established
Existence of modules with large endomorphism algebras shown
Analysis of fields of moduli for these modules conducted
Abstract
We study -elliptic sheaves in terms of their associated modules, which we call Drinfeld-Stuhler modules. We prove some basic results about Drinfeld-Stuhler modules and their endomorphism rings, and then examine the existence and properties of Drinfeld-Stuhler modules with large endomorphism algebras, which are analogous to CM and supersingular Drinfeld modules. Finally, we examine the fields of moduli of Drinfeld-Stuhler modules.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Advanced Algebra and Geometry