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Shiho Lab
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A arithmetic geometry lab that studies algebraic varieties with p-adic tools.
AboutAbout the lab
Studying geometric objects through the p-adic world.
The Shiho Lab studies p-adic objects in arithmetic geometry.
The lab investigates p-adic cohomology and p-adic fundamental groups of (logarithmic) algebraic varieties in positive characteristic.
It also studies p-adic differential equations on (logarithmic) p-adic analytic spaces.
Key terms
- p-adic
- An approach that measures how close two numbers are by looking at how many times they are divisible by a prime p
- Positive characteristic
- A property of number systems (such as finite fields) in which adding 1 to itself a prime number p of times gives 0
- Cohomology
- A tool that extracts properties of a geometric object, such as its holes and how its parts are connected, as algebraic quantities
ResearchResearch themes
The lab studies p-adic objects in arithmetic geometry, focusing on p-adic cohomology and p-adic fundamental groups of algebraic varieties in positive characteristic, and p-adic differential equations on p-adic analytic spaces.
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MembersFaculty
- ProfessorAtsushi ShihoPublications ↗
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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: “Elliptic curve y^2=x^3-x on finite field Z 89” Technopop.tattoo / CC0 (cropped)
- p-adic Objects in Arithmetic Geometry: “3-adic integers” LightbulbMEOW / CC BY-SA 4.0 (cropped)
- Related lab (Imai Lab): “A Klein Quartic embedding in 3D” Ferkel / CC BY-SA 4.0 (cropped)
- Related lab (Tsuji Lab): “Riemann zeta surface” SteJaes / CC BY-SA 4.0 (cropped)
- Related lab (Abe Lab): “3-adic integers” LightbulbMEOW / CC BY-SA 4.0 (cropped)
- Related lab (Saito Lab): “Algebraicszoom” Stephen J. Brooks (talk) Source code in C with OpenGL. / CC BY 3.0 (cropped)
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