[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 60 (1002ﾚｽ)
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341(1): 2021/10/17(日)18:36 ID:dQP0ifDN(16/22) AAS
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つづき
This algorithmic approach is sometimes called monoanabelian. In this thesis we concentrate on the special case when the hyperbolic curve X is a smooth and proper curve of genus one over a p-adic local field K with one K-rational point removed i.e., elliptic curve E punctured at the origin. We consider the problem of reconstructing the local height of a rational point on an elliptic curve from the fundamental group \Pi_X equipped with a section of the absolute Galois group GK determined by this point. We provide such construction for the full e?tale fundamental group of X as well as for its maximally geometrically pro-p quotient in the case when the elliptic curve E has potentially good reduction.
Another problem we consider is determining the reduction type of the elliptic curve E from the maximal geometrically pro-p fundamental group of X, equipped with an additional data of the set of discrete tangential sections. Our main result provides such reconstruction when the residue characteristic p is greater than three. Moreover, we study the tempered fundamental group of a Tate curve and prove that a particular torsor of cohomology classes of theta functions admits a natural trivialization, well defined up to a sign, which is compatible with the integral structure coming form the stable model of the Tate curve. Finally, in the last chapter we shift our attention to studying GK- equivariant automorphisms of various multiplicative submonoids of the monoid (Kalg)× and describe their structure.
外部ﾘﾝｸ:eprints.nottingham.ac.uk
Depositing User: Porowski, Wojciech
Date Deposited: 28 Jul 2020 10:30
Last Modified: 28 Jul 2020 10:45
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342(1): ω1 ◆y7fKJ8VsjM 2021/10/17(日)18:58 ID:w6C+QlCK(13/15) AAS
>>340-341
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