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Hachimori Lab
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A lab that explores the number theory of number fields and elliptic curves through Iwasawa theory.

AboutAbout the lab
Studying the number theory of number fields and elliptic curves.
The Hachimori Lab studies number theory, in particular Iwasawa theory.
Iwasawa theory describes how the Selmer groups and zeta functions attached to number fields and elliptic curves behave over large Galois extensions.
A mysterious relationship is believed to exist between Selmer groups and L-functions, and the lab aims to make this relationship precise in the p-adic setting.
The lab's current research focuses on extending the theory to non-commutative p-adic Lie extensions and to more general Galois representations.
Key terms
- Iwasawa theory
- A theory that describes the behavior of Selmer groups and zeta functions over large Galois extensions
- Selmer group
- An object attached to number fields and elliptic curves. A mysterious relationship with L-functions is believed to exist
- p-adic Lie extension
- A type of non-commutative extension. Efforts are under way to generalize Iwasawa theory to such extensions
ResearchResearch themes
The lab studies Iwasawa theory, which focuses on the Selmer groups and zeta functions attached to number fields and elliptic curves and investigates their behavior over large Galois extensions. It aims to make the mysterious relationship between these two objects of different nature precise in the p-adic setting.
View More ↗MembersFaculty
The lab profile page for the Hachimori Lab lists Associate Professor Yoshitaka Hachimori as a member.
- Associate ProfessorYoshitaka Hachimori
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Secp256k1” https://en.bitcoin.it/wiki/User:Theymos / CC BY-SA 3.0 (cropped)
- Iwasawa theory of Selmer groups and zeta functions: “De Long Room - DPLA - 4a293bd28e3b53c081af01f5355f855c” Brackett, J. Raymond / Public domain (cropped)
- Related lab (加塩研究室): “Spirale Ulam 150” Généré avec la librairie GD de PHP, par Cortexd / Public domain (cropped)
- Related lab (大橋研究室): “Surface sagemath” Kilom691 / CC BY-SA 4.0 (cropped)
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