Organised by
Pol van Hoften and
Lie Qian.
This quarter we are studying moduli "spaces" of p-adic local Galois representations (More precisely, of \'etale phi, Gamma module), also known as the Emerton-Gee stack, following the papers of Emerton and Gee. We aim to understand the construction of this "moduli space" as formal algebraic stacks, its cristalline analogue as p-adic formal algebraic stacks and finally the geometry of its underlying reduced part.
Time: Tuesday 2:30-4:30pm on Zoom and in-person.
Location: 381T at Stanford and Evans 732 at Berkeley.
Seminar Schedule
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(Sep 27th): Overview: motivation and introduction (Pol). Notes
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(Oct 4th): the theory of \'etale $\phi$-modules for $\mathbb{F}_q((t))$ (Daniel). Notes
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(Oct 11th): \'Etale (\varphi, \Gamma)-module and its relation with Galois representation (Stepan).
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(Oct 18th): Breuil-Kisin modules and its relation with cristalline representation (Dong Gyu).
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(Oct 25th): Introduction to algebraic stacks (Xinwen). Notes
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(Nov 1st): Introduction to formal schemes and formal algebraic spaces (Sean).
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(Nov 8th): No Talk. (Democracy Day).
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(Nov 15th): Introduction to algebraic stacks II: Examples and Artin's criterion (Ben).
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(Nov 29th): Wach modules and the proof that $\mathcal{X}$ is an ind-algebraic stack (Pol).
Notes
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(Dec 6th): Construction of the cristalline moduli stack (Mark).
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(Jan 17th): Formal algebraic stacks I (Brian).
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(Jan 31st): Formal algebraic stacks II (Brian).
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(Feb 14th): Herr complexes, and results about cohomology of $\phi, \Gamma$ -modules (Vaughan).
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(Feb 21st): Structure of $\mathcal{X}_d^{\text{red}}$ (Konstantin).
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(Feb 28th): The geometric Breuil-Mezard conjecture (Lie).
References