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Saito Lab
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A number theory and arithmetic geometry lab that studies geometric objects over arithmetic rings.

AboutAbout the lab
Geometry over number theory.
Saito Lab works in arithmetic geometry, studying Galois representations and étale cohomology.
Arithmetic geometry studies geometric objects, such as schemes, defined over arithmetic rings and fields, such as rings of integers and local fields.
The lab studies Galois representations of number fields and local fields, as well as the theory of étale sheaves, which is also used to construct them.
Key terms
- Galois representation
- A representation of the group (the Galois group) formed by the ways the solutions of an equation can be permuted, written in the form of matrices
- Local field
- A field for handling numbers by focusing on a single prime number, such as the field of p-adic numbers
- Scheme
- A generalization of the notion of an algebraic variety that makes it possible to handle geometric objects even over arithmetic rings
ResearchResearch themes
The lab studies geometric objects defined over arithmetic rings and fields, such as rings of integers and local fields. Its research themes are Galois representations of number fields and local fields, and the theory of étale sheaves.
View More ↗MembersFaculty
- ProfessorTakeshi SaitoPublications ↗
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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: “Algebraicszoom” Stephen J. Brooks (talk) Source code in C with OpenGL. / CC BY 3.0 (cropped)
- Galois Representations and Étale Cohomology: “Lattice diagram of Q adjoin a cube root of 2 and a primitive cube root of 1, its subfields, and Galois groups variant” Bender2k14 / CC BY-SA 3.0 (cropped)
- Related lab (Imai Lab): “A Klein Quartic embedding in 3D” Ferkel / CC BY-SA 4.0 (cropped)
- Related lab (Shiho Lab): “Elliptic curve y^2=x^3-x on finite field Z 89” Technopop.tattoo / CC0 (cropped)
- Related lab (Tsuji Lab): “Riemann zeta surface” SteJaes / CC BY-SA 4.0 (cropped)
- Related lab (Ito Lab): “Tetrahedroid” Salix alba / CC BY-SA 4.0 (cropped)
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