Rigid Character Groups, Lubin-Tate Theory, and $(\varphi ,\Gamma )$-Modules Paperback / softback
by Laurent Berger, Peter Schneider, Bingyong Xie
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
The construction of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbf{Q}_p)$ uses in an essential way Fontaine's theory of cyclotomic $(\varphi ,\Gamma )$-modules.
Here cyclotomic means that $\Gamma = \mathrm {Gal}(\mathbf{Q}_p(\mu_{p^\infty})/\mathbf{Q}_p)$ is the Galois group of the cyclotomic extension of $\mathbf Q_p$.
In order to generalize the $p$-adic local Langlands correspondence to $\mathrm{GL}_{2}(L)$, where $L$ is a finite extension of $\mathbf{Q}_p$, it seems necessary to have at our disposal a theory of Lubin-Tate $(\varphi ,\Gamma )$-modules.
Such a generalization has been carried out, to some extent, by working over the $p$-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group.
The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic $(\varphi ,\Gamma )$-modules in a different fashion.
Instead of the $p$-adic open unit disk, the authors work over a character variety that parameterizes the locally $L$-analytic characters on $o_L$.
They study $(\varphi ,\Gamma )$-modules in this setting and relate some of them to what was known previously.
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:75 pages
- Publisher:American Mathematical Society
- Publication Date:30/04/2020
- Category:
- ISBN:9781470440732
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:75 pages
- Publisher:American Mathematical Society
- Publication Date:30/04/2020
- Category:
- ISBN:9781470440732
