STNB 2016 (30th edition)
Modular curves of infinite level.
Co-ordinators
Description
The aim is the study of the local ring at a supersingular point of $X(p^{\infty})$, the inverse limit when $n$ tends to infinite of the classical modular curves $X(p^n)$.
Such ring has an interpretation as a deformation ring of a supersingular curve joint with a $\mathbb{Z}_p$-basis of its Tate module. The theory of perfectoides spaces helps to understand easily such moduli spaces of infinite level than the understanding of the analogue ones in finite level.
Talks
- Introducció a les corbes modulars de nivell infinit (Xavier Guitart)
- Grups p-divisibles, grups formals i deformacions (Eduard Soto)
- Espais de Lubin-Tate de nivell infinit (Santiago Molina Blanco)
- Espais àdics i espais perfectoides (Alberto Cámara)
- Models estables de corbes de nivell infinit (Xavier Xarles)
References
Peter Scholze, Perfectoid spaces, Publ. Math. Ins. Hautes Etudes Sci. 116(2012), 245-313. MR3090258
Jared Weinstein, Modular curves at infinite level, notes for the lecture series at the 2013 Arizona Winter School in Tucson. Available at http://math.bu.edu/people/jsweint/AWS/AWSLectureNotes.pdf
Jared Weinstein, Semistable models for modular curves of arbitrary level, 2014. Available at http://math.bu.edu/people/jsweint/StableReduction/StabRed2012.pdf
James Weinstein, Notes from Peter Scholze's revolutionary course on p-adic geometry. Available at https://math.berkeley.edu/~jared/Math274/ScholzeLectures.pdf
