From modular curves to Shimura curves: a p-adic approach

Reference : From modular curves to Shimura curves: a p-adic approach


	Document type :	Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/29872

Title :	From modular curves to Shimura curves: a p-adic approach
Language :	English
Author, co-author :	Amoros Carafi, Laia [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	24-Nov-2016
Audience :	International
Event name :	Our Mathematics Spectrum
Event date :	24-11-2016
Event organizer :	University of Luxembourg
Event place (city) :	Luxembourg
Keywords :	[en] modular curves ; Shimura curves ; bad reduction
Abstract :	[en] Shimura curves arise as a natural generalisation of elliptic curves. As modular curves, they are constructed as Riemann surfaces, and they turn out to have structure of algebraic curve, i.e. they can be described by some algebraic equations with coefficients in some finite extension of Q. Number theorists are interested in the reductions modulo p of these equations. The problem is that these equations are very difficult to compute. I will describe a method to find these reductions without actually knowing the equation.
Permalink :	http://hdl.handle.net/10993/29872

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