<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">D</mml:mi></mml:math>-elliptic sheaves and odd Jacobians

Papikian, Mihran

doi:10.1016/j.jnt.2012.02.005

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2019

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“…Over the years, the third author of this paper have studied the arithmetic properties of D-elliptic sheaves and their modular varieties, trying to extend to this setting the rich theory of abelian surfaces with quaternionic multiplication and Shimura curves; see, for example, [19], [20], [21], [22], [23], [24], [25]. The current paper is a natural continuation of [25].…”

Section: Introductionmentioning

confidence: 99%

Drinfeld-Stuhler modules and the Hasse principle

Arai¹,

Kondo²,

Papikian³

2019

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We develop a theory of canonical isogeny characters of Drinfeld-Stuhler modules similar to the theory of canonical isogeny characters of abelian surfaces with quaternionic multiplication. We then apply this theory to give explicit criteria for the non-existence of rational points on Drinfeld-Stuhler modular varieties over the finite extensions of F q (T ). This allows us to produce explicit examples of Drinfeld-Stuhler curves violating the Hasse principle.

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