SeZoom

This is the website for our learning seminar on Serre’s book “Abelian \(\ell\)-Adic Representations and Elliptic Curves” and the related Inventiones paper (see this translation by Pete Clark). We will meet on Fridays at 4pm; the schedule is below.

• 1/15/2021 - Brief organizational meeting

• 1/22/2021 - Intro (Daniel)

• 1/29/2021 - \(\ell\)-adic representations (Serre I.1 and I.2) (Santana)

• 2/12/2021 - 430pm (note unusual time) - Talk overflow time, I.2.Appendix, exercise discussion

• 2/19/2021 - Construction of tori (Serre II.1 and II.2) (Sasha)

• 2/26/2021 - Structure theory (Serre II.3 and II.Appendix) (Nicholas - notes)

• 3/5/2021 - Overflow time, exercise discussion

• 3/12/2021 - Locally algebraic representations (Serre III.1-3) (Freddy)

• 3/19/2021 - Hodge-Tate theory (III.Appendix and other sources) (Padma - notes)

• 3/26/2021 - Discussion and exercises

• 4/2/2021 - Preliminaries and Shafarevich’s theorem (Serre IV.1 and other sources) (Arvind)

• 4/9/2021 - Serre IV.2-3 (finishing the proof) (Mentzelos)

• 4/16/2021 - Serre IV.Appendix (Borys, tentative)

• 4/23/2021 - Discussion and exercises

• 4/30/2021 - Serre’s Inventiones paper (Tyler)

• 5/7/2021 - Tate conjecture for Abelian varieties over finite fields (Haiyang)

• 5/14/2021 - mystery topic (maybe Hodge-Tate decomposition?) (Daniel)

• Other possible topics: Sharevich conjecture, a bit of p-adic Hodge theory, Hodge-Tate theory for Abelian varieties, Bogomolov’s open image theorem