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Algebra 1 (Number Theory) Lab (Ito)
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A lab that studies geometric objects in positive characteristic through arithmetic geometry.
AboutAbout the lab
Counting solutions of equations through the eyes of geometry.
The Ito Lab studies arithmetic geometry within number theory.
One of its research themes is the weight-monodromy conjecture in equal characteristic.
In collaborative research, the lab investigates curves over finite fields and the properties of varieties in positive and mixed characteristic.
Key terms
- Arithmetic geometry
- A field that studies solutions of equations over the integers or finite fields as geometric properties of shapes
- Positive characteristic
- A number system, like a finite field, in which adding 1 to itself a prime number p of times gives 0
- L-polynomial
- A polynomial that collects, in a single expression, information about the number of points on a curve over a finite field
ResearchResearch themes
The lab studies arithmetic geometry, including the weight-monodromy conjecture in equal characteristic and curves and varieties in positive characteristic.
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MembersFaculty
- Associate ProfessorTetsushi Ito
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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: “EllipticGroup” Thomas Cooper / Public domain (cropped)
- Curves in Positive Characteristic and L-polynomials: “Elliptic curve y^2=x^3-x on finite field Z 61” Technopop.tattoo / Public domain (cropped)
- Related lab (Geometry 2 (Discrete Group Theory) Lab): “Loop erased random walk in 2D” Cosmia Nebula / CC BY-SA 4.0 (cropped)
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- Related lab (Applied Mathematics Lab (Partial Differential Equations, Inverse Problems) (Yikan Liu)): “Schematic illustration of CT scanner, extracted from Policy implications of the computed tomography (CT) scanner (1978)” Congress of the United States, Office of Technology Assessment / Public domain (cropped)
- Related lab (Algebra 1 (Number Theory) Lab (Atobe)): “Bruhat-Tits-tree-for-Q-2” 부고 / CC BY-SA 4.0 (cropped)
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