Equidimensional adic eigenvarities for groups with discrete series

Author: 

Gulotta, D

Publication Date: 

9 October 2019

Journal: 

Algebra and Number Theory

Last Updated: 

2021-07-20T05:06:48.5+01:00

Issue: 

8

Volume: 

13

DOI: 

10.2140/ant.2019.13.1907

page: 

1907-1940

abstract: 

<p style="text-align:justify;"> We extend Urban’s construction of eigenvarieties for reductive groups <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> such that <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mrow><mo class="MathClass-open">(</mo><mrow><mi>ℝ</mi></mrow><mo class="MathClass-close">)</mo></mrow></math> has discrete series to include characteristic <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> points at the boundary of weight space. In order to perform this construction, we define a notion of “locally analytic” functions and distributions on a locally <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> -analytic manifold taking values in a complete Tate <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>ℤ</mi></mrow><mrow><mi>p</mi></mrow></msub></math> -algebra in which <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> is not necessarily invertible. Our definition agrees with the definition of locally analytic distributions on <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> -adic Lie groups given by Johansson and Newton. </p>

Symplectic id: 

1033660

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article