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Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

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Number Theory Problem for 1st/2nd Year Graduate Student

I am looking for a problem in (algebraic) number theory in which a 1st/2nd year graduate student in number theory can make some nontrivial progress. I am not looking for something that can conceivably …