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Title: Modular curves and Néron models of generalized Jacobians
Let$$X$$be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring$$R$$, and$$\mathfrak {m}$$a modulus on$$X$$, given by a closed subscheme of$$X$$which is geometrically reduced. The generalized Jacobian$$J_\mathfrak {m}$$of$$X$$with respect to$$\mathfrak {m}$$is then an extension of the Jacobian of$$X$$by a torus. We describe its Néron model, together with the character and component groups of the special fibre, in terms of a regular model of$$X$$over$$R$$. This generalizes Raynaud's well-known description for the usual Jacobian. We also give some computations for generalized Jacobians of modular curves$$X_0(N)$$with moduli supported on the cusps.  more » « less
Award ID(s):
1646385
PAR ID:
10553548
Author(s) / Creator(s):
; ;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
Compositio Mathematica
Volume:
160
Issue:
5
ISSN:
0010-437X
Page Range / eLocation ID:
945 to 981
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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