scholarly journals Invariants of Some Algebraic Curves Related to Drinfeld Modular Curves

2001 ◽  
Vol 90 (1) ◽  
pp. 166-183 ◽  
Author(s):  
Ernst-Ulrich Gekeler
Keyword(s):  
Algebraic Curves ◽  
Modular Curves ◽  
Drinfeld Modular Curves

Rational torsion of generalized Jacobians of modular and Drinfeld modular curves

2019 ◽  
Vol 31 (3) ◽  
pp. 647-659
Author(s):  
Fu-Tsun Wei ◽  
Takao Yamazaki
Keyword(s):  
Prime Power ◽  
Analogous Result ◽  
Power Level ◽  
Modular Curves ◽  
Generalized Jacobian ◽  
Torsion Points ◽  
Modular Curve ◽  
Generalized Jacobians ◽  
Drinfeld Modular Curves ◽  
Primary Torsion

Abstract We consider the generalized Jacobian {\widetilde{J}} of the modular curve {X_{0}(N)} of level N with respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly determine the structure of the {\mathbb{Q}} -rational torsion points on {\widetilde{J}} up to 6-primary torsion. The result depicts a fuller picture than [18] where the case of prime power level was studied. We also obtain an analogous result for Drinfeld modular curves. Our proof relies on similar results for classical Jacobians due to Ohta, Papikian and the first author. We also discuss the Hecke action on {\widetilde{J}} and its Eisenstein property.

scholarly journals On plane models for Drinfeld modular curves

2006 ◽  
Vol 119 (1) ◽  
pp. 18-27
Author(s):  
So Young Choi ◽  
Kuk Jin Hong ◽  
Daeyeol Jeon
Keyword(s):  
Modular Curves ◽  
Drinfeld Modular Curves

scholarly journals ON THE EISENSTEIN IDEAL OF DRINFELD MODULAR CURVES

2007 ◽  
Vol 03 (04) ◽  
pp. 557-598 ◽  
Author(s):  
AMBRUS PÁL
Keyword(s):  
Prime Ideal ◽  
Hecke Algebra ◽  
General Characteristic ◽  
Drinfeld Modules ◽  
Modular Curves ◽  
Characteristic P ◽  
Modular Curve ◽  
Drinfeld Modular Curves ◽  
Eisenstein Ideal

Let 𝔈(𝔭) denote the Eisenstein ideal in the Hecke algebra 𝕋(𝔭) of the Drinfeld modular curve X0(𝔭) parameterizing Drinfeld modules of rank two over 𝔽q[T] of general characteristic with Hecke level 𝔭-structure, where 𝔭 ◃ 𝔽q[T] is a non-zero prime ideal. We prove that the characteristic p of the field 𝔽q does not divide the order of the quotient 𝕋(𝔭)/𝔈(𝔭) and the Eisenstein ideal 𝔈(𝔭) is locally principal.

scholarly journals On component groups of Jacobians of Drinfeld modular curves

2004 ◽  
Vol 54 (7) ◽  
pp. 2163-2199 ◽  
Author(s):  
Mihran Papikian
Keyword(s):  
Modular Curves ◽  
Drinfeld Modular Curves
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