## Department of Mathematics

Indian Institute Of Technology Madras , Chennai

### Arakelov Geometry of Modular Curves $X_0(p^2)$

#### Abstract :

We shall explore the geometry of the Modular curve $X_0(p^2)$ and it's regular minimal model over the ring of integers, which is an arithmetic surface. After a base change we shall show that the regular minimal model is semi-simple. Arakelov has introduced an intersection pairing for divisors on arithmetic surfaces. We shall derive an expression for the Arakelov self-intersection of the relative dualising sheaf on the regular minimal model of $X_0(p^2)$. As a consequence, we shall give some number theoretic applications for this computation. This is a joint work with Debargha Banerjee and Diganta Borah

Key Speaker Dr. Chitrabhanu Chaudhuri, Department of mathematics (IISER Pune)
Place NAC 522
Start Time 11:00 AM
Finish Time 11:50 AM