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A path towards semistable models of smooth projective curves over \(\mathbb{Q}\)
I hold a master seminar that aim to study models of smooth projective curves over \(\mathbb{Q}\). The goal that moves us is to reach the existence of semistable models over an affine Dedeking scheme of dimension \(1\) of fibered surfaces with smooth projective generic fiber. As this is obviously a lot of big bad words, we will stop during our walk to glimpse various notions in algebraic geometry and compute precise examples. We will also end by three more introductive talks about (newer) alternative ways to think about this problem : shifting our geometry theories to formal schemes and Berkovich spaces.
The seminar is held on Tuesdays between 2:00 - 4:00 p.m. in SR 1C. You should register on the intranet. You can find back all informations on the same link.
The seminar is held on Tuesdays between 2:00 - 4:00 p.m. in SR 1C. You should register on the intranet. You can find back all informations on the same link.
Resources :
- Program of the seminar : pdf.
Bibliography :
- A. Ducros: Introduction à la théorie des schémas, lecture notes, pdf link.
- A. Ducros: La structure des courbes analytiques, draft of a book, pdf link.
- A. Ducros: Espaces Analytiques \(p\)-adiques au sens de Berkovich, talk n°958 of the Bourbaki seminar, 2006, pdf link.
- K. Fujiwara and F. Kato: Foundations of Rigid Geometry I, European Math. Soc., 2018, arXiV link.
- L. Illusie: Grothendieck's existence theorem in formal geometry, online notes for Advanced School in Basic Algebraci Geometry, 2003, pdf link.
- Q. Liu: Algebraic Geometry and Arithmetic Curves, Oxford University Press, 2002, pdf link.
- J. Poineau: Raconte-moi... la droite de Berkovich, Gazette de la S.M.F., 2016, S.M.F. link.
- The Stacks Project, link to the welcome page.