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| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
2023年05月10日(水)
17:00-18:00 数理科学研究科棟(駒場) 117号室
Guy Henniart 氏 (パリ第11大学)
Swan exponent of Galois representations and fonctoriality for classical groups over p-adic fields (English)
Guy Henniart 氏 (パリ第11大学)
Swan exponent of Galois representations and fonctoriality for classical groups over p-adic fields (English)
[ 講演概要 ]
This is joint work with Masao Oi in Kyoto. Let F be a p-adic field for some prime number p,
F^ac an algebraic closure of F, and G_F the Galois group of F^ac/F. A continuous finite dimensional
representation σ (on a complex vector space W) has a Swan exponent s(σ), a non-negative integer
which measures how "wildly ramified" σ is. Langlands functoriality makes it of interest
to compare s(σ) and s(r o σ) when r is an algebraic representation of Aut_C(W). The first cases
for r are the determinant, the adjoint representation, the symmetric square representation and
the alternating square representation. I shall give some relations (inequalities mostly, with
equality in interesting cases) between the Swan exponents of those representations r o σ. I shall
also indicate how such relations can be used to explicit the local Langlands correspondence of
Arthur for some simple cuspidal representations of split classical groups over F.
This is joint work with Masao Oi in Kyoto. Let F be a p-adic field for some prime number p,
F^ac an algebraic closure of F, and G_F the Galois group of F^ac/F. A continuous finite dimensional
representation σ (on a complex vector space W) has a Swan exponent s(σ), a non-negative integer
which measures how "wildly ramified" σ is. Langlands functoriality makes it of interest
to compare s(σ) and s(r o σ) when r is an algebraic representation of Aut_C(W). The first cases
for r are the determinant, the adjoint representation, the symmetric square representation and
the alternating square representation. I shall give some relations (inequalities mostly, with
equality in interesting cases) between the Swan exponents of those representations r o σ. I shall
also indicate how such relations can be used to explicit the local Langlands correspondence of
Arthur for some simple cuspidal representations of split classical groups over F.
