Seminars Sorted by Series

From Romyar's AWS notes:

• Section 5.1, especially: Prop 5.1.5, Cor 5.1.9, Rem 5.1.10, Ex 5.1.11

From McCallum-Sharifi:

• Explain why $\mathbb{Q}(37^{1/37})$ has class number prime-to-37 (this is Cor 7.6). It may simplify the proof to use Cor 5...

Forthcoming work of Sharifi-Venkatesh.

From Romyar's AWS notes:

• Sections 4.1 and 4.2.

Regarding the proof of Ohta's comparison isomorphism:

• Discuss Fukaya-Kato Section 1.7, which explains some p-adic Hodge theory background.
• Discuss some elements of Ohta's proof, from Sections 3...

Introduce the L-function, and then the p-adic L-function, of a cusp form, and the of a Hida family of cups forms. What we need is in Fukaya-Kato Sections 4.4-4.5. See also: Mazur-Tate-Teitelbaum and Mazur's "Anomalous eigenforms" note.

State the main theorems of Fukaya-Kato and outline the proofs.

Give the details of the proof of "Theorem A" from week ten. Fukaya-Kato sections 6.3, 9.1-9.5.

We will talk about the categorification of the positive half of the quantum group $\mathbb{U}_q(\mathfrak{sl}_2)$ using the module categories over NilHecke algebras. We hope to explain the idea of categorification using this example.

It is well known that representations of open compact subgroups (called types) play a fundamental role in studying representations of $p$-adic groups. We give an overview of the theory (after Bernstein, Moy-Prasad, Bushnell-Kutzko) in connection...