Arithmetic deformation to the normal cone

Reading seminar, Fall 2024, Leiden University.
Organisers: Robin de Jong, Emre Can Sertöz

Short summary

The first half of the seminar will be introductory, with lectures covering classical intersection theory, deformation to the normal cone, and arithmetic intersection theory (following Gillet-Soulé). In the second half, we will study the PhD thesis of Junda Hu, a former student of Gillet, which provides the arithmetic analogue for deformation to the normal cone. Since the thesis has not been published, it is not fully polished, and our goal is to clarify the constructions for better conceptual understanding and computational ease. We intend to explore the behavior of arithmetic self-intersections.

We note that there is currently no formula for self-intersections in arithmetic geometry that utilizes the normal bundle. We will keep this in mind as we work toward such a development. Additionally, we hope to generalize our previous work with Bloch, which relates arithmetic heights to the heights of limit mixed Hodge structures. We believe that Junda Hu’s construction holds the key.

Detailed program

Read the detailed program for the seminar on Overleaf (no account required).

Time table

All lectures take place on Mondays, 14:15–16:00 in the Gorlaeus building. Please check the schedule below for the lecture rooms. (Exception: Talk 6 in Huygens.)

Each week, we will have a single talk of 2×45 minutes with a 15 minute break between the two halves.

Week #	Date (2024)	Room	Seminar	Speaker
40	Sept 30	BW 0.31	Talk 1	Robin de Jong
41	Oct 7	BW 0.31	Talk 2	Stijn Velstra
42	Oct 14	DM 1.15	Talk 3	Amira Tlemsani
43	Oct 21	X	No seminar	X
44	Oct 28	DM 1.09	Talk 4	Tom Manopulo
45	Nov 4	DM 1.09	Talk 5	Zhelun Chen
46	Nov 11	Room 2.04 in the Huygens	Talk 6	David Lilienfeldt
47	Nov 18	DM 1.09	Talk 7	Jan Vonk
48	Nov 25	BM 2.26	Talk 8 (notes)	Riccardo Pengo
49	Dec 2	BW.2.18.a	Talk 9 (notes)	Riccardo Pengo
50	Dec 9	BM 2.26	Talk 10	Riccardo Pengo
51	Dec 16	BW 0.31	Talk 11	Emre Can Sertöz