

LFunctions and Algebraic Varieties. A conference in memory of Alexey Zykin
February 8, 2018 14:30–15:30, Moscow, Moscow Independent University, 11 Bolshoi Vlassievsky per.






A BrauerSiegel theorem for an ArtinSchreier family of elliptic curves
Richard Griffon^{} 
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Abstract:
The classical BrauerSiegel theorem gives upper and lower bounds on the product of the classnumber times the regulator of units of a number field, in terms of its discriminant. Now consider an elliptic curve E defined over $F_q (t)$: one can form the product of the order of the TateShafarevich group of E (assuming it is finite) and of its NéronTate regulator. We are interested in finding upper and lower bounds of this quantity in terms of simpler invariants of E, e.g. its height. In general this question is open, and has a satisfactory answer in only a handful of cases. In this talk, I will report on a recent work where I studied an "ArtinSchreier family" of elliptic curves. I will explain how good unconditional bounds can be found in this case. This provides a new example of family of elliptic curves for which an analogue of the classical BrauerSiegel theorem holds. T.B.A.

