分野別セミナー

Recently Coleman-McMurdy found the stable reduction of $X_0(p^3)$ based on rigid geometry and using Gross-Hopkins theory to analyze the supersingular locus. Furthermore, McMurdy conjecture on the stable reduction of $X_0(p^4).$
We found an explicit computation of ``new components'' found by Coleman-McMurdy in the stable reduction of $X_0(p^3)$ without using Gross-Hopkins theory.
We found new components appearing in the stable reduction in $X_0(p^4)$ which does not appear in the conjecture of McMurdy.
We will talk on these topics.