Non-admissible modulo p representations of GL_2(Q_{p^2})

Seminar
Speaker
Prof. Eknath Ghate (Tata Institute of Fundamental Research, Mumbai)
Date
19/08/2020 - 11:30 - 10:30Add to Calendar 2020-08-19 10:30:00 2020-08-19 11:30:00 Non-admissible modulo p representations of GL_2(Q_{p^2}) The notion of admissibility of representations of p-adic groups    goes back to Harish-Chandra. Jacquet and Vigneras have shown that    smooth irreducible representations of connected reductive p-adic    groups over algebraically closed fields of characteristic different    from p are admissible.      The smooth irreducible representations of $\mathrm{GL}_2({\mathbb Q}_p)$    over $\bar{\mathbb F}_p$ are also known to be admissible, by the    work of Barthel-Livne, Breuil and Berger.  However, recently Daniel Le    constructed non-admissible smooth irreducible representations of    $\mathrm{GL}_2({\mathbb Q}_{p^f})$ over $\bar{\mathbb F}_p$    for f > 2, where ${\mathbb Q}_{p^f}$ is the unramified extension    of ${\mathbb Q}_p$ of  degree f. His construction uses a    diagram (in the sense of Breuil and Paskunas) attached to    an irreducible mod p representation of the Galois group of    ${\mathbb Q}_{p^f}$.      We shall speak about a variant of Le's construction in the case f = 2    which uses instead a diagram attached to a reducible split representation    of the Galois group of ${\mathbb Q}_{p^2}$. This is joint work    with Mihir Sheth.   ======================================= Michael Schein is inviting you to a scheduled Zoom meeting.   Topic: BIU Algebra Seminar -- Ghate Time: Aug 5, 2020 10:00 AM Jerusalem   Join Zoom Meeting https://zoom.us/j/3185323623?pwd=NzJncWZVV1dJQXZSSDlralk1d3NsZz09   Meeting ID: 318 532 3623 Passcode: 142857 Zoom invitation below אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Zoom invitation below
Abstract

The notion of admissibility of representations of p-adic groups

   goes back to Harish-Chandra. Jacquet and Vigneras have shown that

   smooth irreducible representations of connected reductive p-adic

   groups over algebraically closed fields of characteristic different

   from p are admissible.

 

   The smooth irreducible representations of $\mathrm{GL}_2({\mathbb Q}_p)$

   over $\bar{\mathbb F}_p$ are also known to be admissible, by the

   work of Barthel-Livne, Breuil and Berger.  However, recently Daniel Le

   constructed non-admissible smooth irreducible representations of

   $\mathrm{GL}_2({\mathbb Q}_{p^f})$ over $\bar{\mathbb F}_p$

   for f > 2, where ${\mathbb Q}_{p^f}$ is the unramified extension

   of ${\mathbb Q}_p$ of  degree f. His construction uses a

   diagram (in the sense of Breuil and Paskunas) attached to

   an irreducible mod p representation of the Galois group of

   ${\mathbb Q}_{p^f}$.

 

   We shall speak about a variant of Le's construction in the case f = 2

   which uses instead a diagram attached to a reducible split representation

   of the Galois group of ${\mathbb Q}_{p^2}$. This is joint work

   with Mihir Sheth.

 

=======================================

Michael Schein is inviting you to a scheduled Zoom meeting.

 

Topic: BIU Algebra Seminar -- Ghate

Time: Aug 5, 2020 10:00 AM Jerusalem

 

Join Zoom Meeting

https://zoom.us/j/3185323623?pwd=NzJncWZVV1dJQXZSSDlralk1d3NsZz09

 

Meeting ID: 318 532 3623

Passcode: 142857

Last Updated Date : 29/07/2020