Báo cáo khoa học 演講訊息

The class group of the ring of integers in a number field or a function field is a finite abelian group that measures how far this ring is from having unique factorization into prime elements. Class groups are a central object in Algebraic Number Theory, with applications ranging from Fermat's Last Theorem to cryptography. We discuss some open questions concerning the existence of class groups with high m-rank and give some partial answers in the function field case.