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KIAS Intensive Lecture Series on
Rigid Geometry and the Local Langlands Correspondence
Jan 02 – 05, 2012 / KIAS seminar room (5th floor)
Program Description
The local Langlands correspondence (LLC) is of fundamental importance in number theory and representation theory and has triggered many new developments in modern number theory in the last few decades. The LLC for GL(n) over padic fields has been established a little more than 10 years ago by HarrisTaylor and Henniart. A crucial idea, originating from Deligne, Drinfeld and Carayol, is to exploit the ladic etale cohomology theory for padic algebraic geometry (where l is a prime different from p) to study and establish LLC. The geometric objects in this story are certain moduli spaces of pdivisible groups and can be viewed as padic rigid analytic spaces. (They are called LubinTate spaces, or RapoportZink spaces in the more general context.) Thus their etale cohomology and its representationtheoretic description are at the core of interest for number theorists and representation theorists alike.
The ladic cohomology theory for rigid spaces is exciting on its own right with diverse applications in algebraic geometry. Rigid geometry is appealing to complex algebraic geometers for its resemblance and intriguing for its unique features not present in the complex analogue.
The key component in the intensive lecture series is Mieda's lectures on etale cohomology on rigid spaces (four 90 minute lectures). In the accompanying lectures, there will be an expository talk introducing the audience to LLC as well as the application of rigid geometry to LLC.
Invited Speakers
Tetsushi Ito (Kyoto)
Yoichi Mieda (Kyushu)
Sug Woo Shin (MIT/KIAS)
Teruyoshi Yoshida (Camridge)
Organizers
YounSeo Choi (KIAS)
Sug Woo Shin (MIT/KIAS)
