Parabolic Simple $\mathcal{L}$-invariants and Local-global Compatibility -

Parabolic Simple $L$ -invariants and Local-global Compatibility

发布时间：2022年11月11日浏览次数：3715 发布者: He Liu

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主讲人： Yiqin He (PKU)

活动时间： 从 2022-11-14 11:00 到 12:00

场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室

Let

L

be a finite extension of

Q_{p}

and

ρ_{L}

be a potentially semistable noncrystalline

p

-adic representation of

{Gal}_{L}

such that the associated

F

-semisimple Weil-Deligne representation is absolutely indecomposable. Via a study of Breuil's parabolic simple

L

-invariants, we attach to

ρ_{L}

a locally

Q_{p}

-analytic representation

Π (ρ_{L})

{GL}_{n} (L)

, which carries the exact information of the Fontaine-Mazur parabolic simple

L

-invariants of

ρ_{L}

. When

ρ_{L}

comes from a patched automorphic representation of

G (A_{F^{+}})

(for a unitary group

G

over a totally real field

F^{+}

which is compact at infinite places and

{GL}_{n}

p

-adic places), we prove under mild hypothesis that

Π (ρ_{L})

is a subrepresentation of the associated Hecke-isotypic subspace of the Banach spaces of (patched)

p

-adic automophic forms on

G (A_{F^{+}})

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