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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 296: Graduate Student Colloquium
Prof. Kiran Kedlaya
UC San Diego
Counting curves (and their rational points) over finite fields
Abstract:
For q a prime power, let F_q be the finite field of order q. There are a finite number of isomorphism classes of (smooth, projective, geometrically irreducible) curves of genus g over F_q. Can one give a closed form expression for this number? We discuss how to correctly interpret this question; how to generalize it by also counting marked points; what is known for small g; and what information can be gained by making complete tables of curves of a given genus.
April 22, 2025
3:00 PM
APM 6402
Research Areas
Algebraic Geometry Number Theory****************************
