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SUMMARY:Santosh Nadimpalli (IIT Kanpur)
DTSTART:20200501T110000Z
DTEND:20200501T120000Z
DTSTAMP:20260423T040003Z
UID:NTdL/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTdL/1/">Lin
 kage principle and base change for ${\\rm GL}_2$</a>\nby Santosh Nadimpall
 i (IIT Kanpur) as part of Number theory during lockdown\n\n\nAbstract\nLet
  $l$ and $p$ be two distinct odd primes. Let $F$ be a finite extension of 
 $Q_p$\, and let $E$ be a finite Galois extension of $F$ with $[E: F]=l$.\n
 Let $(\\pi\, V)$ be a cuspidal representation of ${\\rm GL}_2(F)$ with an\
 nintegral central character. Let $(\\pi_E\, W)$ be the ${\\rm GL}_2(E)$\nr
 epresentation obtained by base change of $\\pi$. The Galois group of $E/F$
 \,\ndenoted by $G$\, acts on $\\pi_E$. We show that the zeroth Tate cohomo
 logy\ngroup of $\\pi_E$\, as a $G$-module\, is isomorphic to the Frobenius
  twist of\nthe mod-$l$ reduction of $\\pi_F$. We use Kirillov model to pro
 ve this\nresult. The first half of the lecture will be a review of some pr
 eliminary\nresults on Kirillov model\, and in the latter half\, I will exp
 lain the proof\nof the above result.\n
LOCATION:https://researchseminars.org/talk/NTdL/1/
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