Directions in Number Theory: Proceedings of the 2014 WIN3 - download pdf or read online

By Ellen E. Eischen, Ling Long, Rachel Pries, Katherine E. Stange

ISBN-10: 3319309749

ISBN-13: 9783319309743

ISBN-10: 3319309765

ISBN-13: 9783319309767

Exploring the interaction among deep conception and complex computation, this quantity is a compilation of analysis and survey papers in quantity conception, written by means of participants of the ladies In Numbers (WIN) community, mostly via the collaborative study teams shaped at ladies In Numbers three, a convention on the Banff overseas examine Station in Banff, Alberta, on April 21-25, 2014. The papers span quite a lot of study components: mathematics geometry; analytic quantity conception; algebraic quantity thought; and functions to coding and cryptography.
The WIN convention sequence started in 2008, with the purpose of strengthening the learn careers of woman quantity theorists. The sequence brought a unique research-mentorship version: girls in any respect profession levels, from graduate scholars to senior contributors of the neighborhood, joined forces to paintings in targeted examine teams on state of the art initiatives designed and led by means of skilled researchers. The objectives for ladies In Numbers three have been to set up formidable new collaborations among ladies in quantity idea, to coach junior individuals approximately themes of present significance, and to proceed to construct a colourful group of ladies in quantity concept. Forty-two girls attended the WIN3 workshop, together with 15 senior and mid-level college, 15 junior school and postdocs, and 12 graduate students.

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Extra info for Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop

Example text

Then is the unique (up to scaling) non-trivial anticyclotomic p-adic idele class character. S. Balakrishnan et al. 6. Note that W A =K ! 1. K/ and compute the kernel of this pairing. 7. 5. 5. For any finite prime w of K, the natural inclusion Kw ,! A induces a map Ãw W Kw ! K/, and we write w D ı Ãw . P/ as a local denominator of P at w. P/ follows from the Weierstrass equation for E and the fact that Ow is a principal ideal domain. Finally, we let denote the -adic -function of E. P/ D . P// . P/.

K/ ! Qp . The kernel of such a (non-zero) Qp -linear map corresponds to a Zp -extension of K. In particular, the anticyclotomic Zp -extension of K corresponds to a Qp -linear , where c denotes complex conjugation. K/ ! Qp such that ı c D The resulting anticyclotomic p-adic height pairing is denoted by . ; / . One key step of our work is an explicit description of the map , see Sect. 2. P; P/ . Mazur et al. P/ D . P// . P//; w−p1 where is one of the prime divisors of p in K and the remaining notation is defined in Sect.

7 G14 F14 ! 7 G13 F11 7! G11 F5 7! G6 C5 7! C6 F6 7! G6 C6 7! e D6 F7 7! G7 F9 7! G9 F14 7! G14 F5 7! G5 C5 7! e D5 C7 ! 7 D7 C9 ! 7 D9 F2 $ F3 C2 $ C3 F10 7! G10 F1 $ G1 Action on Pic Y a C1 7! D1 D1 $ e C1 C2 7! e C2 C3 7! e C3 Action on Pic X a P3 $ P4 Q1 $ Q3 Q2 $ Q4 Action on Weierstrass points i c q p 10 ab c p 10 ab p a Á0 Â0 7! Â0 ÂiC 7! Âi 7! q p a 7! Á0 7! p 2C2 2 q p 7! 2C2 2 p p c 7! c q i 7! Action on splitting field C8 $ C9 C6 7! D6 C5 7! D5 C6 7! D6 C5 7! D5 C4 ! 7 D4 C6 ! 7 D6 C7 7!

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Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop by Ellen E. Eischen, Ling Long, Rachel Pries, Katherine E. Stange

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