Projects in Mathematics Muenster

Research area A: Arithmetic and Groups
Unit A1: Arithmetic, geometry and representations

Further Projects
CRC 1442: Geometry: Deformation and Rigidity - A01: Automorphic forms and the p-adic Langlands programme The p-adic Langlands programme aims to establish a relation between p-adic representations of p-adic reductive groups and p-adic representations of Galois groups of p-adic local fields. We plan an in depth study of the smooth mod p representation theory of reductive groups on the level of derived categories. In first relevant test cases we want to construct functors from representations of reductive groups to sheaves on deformation spaces of Galois representations. online
CRC 1442: Geometry: Deformation and Rigidity - A02: Moduli spaces of p-adic Galois representations p-adic Galois representations in finite Zp-modules are equivalent to (phi,Gamma)-modules for Qp. In this project, we develop the theory of (phi,Gamma)-modules further in the direction of finite extensions of Qp and their function field analogues. We will also use (phi,Gamma)-modules to construct moduli spaces of p-adic Galois representations. We aim to decompose special fibres on these moduli spaces into cycles in a way that mirrors multiplicity formulas in representation theory. online

Research Interests

Research Interests

$\bullet$ Algebraic number theory.
$\bullet$ Arithmetic geometry.
$\bullet$ Representation theory.
$\bullet$ $p$-Adic analysis.

Selected Publications

Selected Publications of Peter Schneider

$\bullet$ P. Schneider. Smooth representations and Hecke modules in characteristic $p$. Pacific J. Math., 279:447–464, 2015.

$\bullet$ R. Ollivier and P. Schneider. Pro-$p$- Iwahori- Hecke algebras are Gorenstein. J. Inst. Math. Jussieu, 13:753–809, 2014.

$\bullet$ P. Schneider. $p$-adic Lie groups, volume 344 of Grundlehren der Mathematischen Wissenschaften [A Series of Comprehensive Studies in Mathematics]. Springer Berlin Heidelberg, 2011.

$\bullet$ C. Breuil and P. Schneider. First steps towards $p$-adic Langlands functoriality. J. Reine Angew. Math., 610:149–180, 2007.

$\bullet$ P. Schneider and J. Teitelbaum. Banach- Hecke algebras and $p$-adic Galois representations. Documenta Mathematica, The Book Series 4 (J. {Coates' Sixtieth Birthday)}, 4:631–684, 2006.

$\bullet$ P. Schneider and J. Teitelbaum. Algebras of $p$-adic distributions and admissible representations. Invent. Math., 153:145–196, 2003.

$\bullet$ P. Schneider and J. Teitelbaum. Locally analytic distributions and $p$-adic representation theory, with applications to $GL_2$. J. AMS, 15:443–468, 2002.

$\bullet$ P. Schneider and J. Teitelbaum. Banach space representations and Iwasawa theory. Israel J. Math., 127:359–380, 2002.

$\bullet$ P. Schneider and J. Teitelbaum. $p$-adic Fourier theory. Documenta math., 6:447–481, 2001.

$\bullet$ P. Schneider and U. Stuhler. Representation theory and sheaves on the Bruhat- Tits building. Publ. Math. IHES, 85:97–191, 1997.

Current Publications

$\bullet $ Peter Schneider and Claus Sorensen. Duals in natural characteristic. arXiv e-prints, February 2022. arXiv:2202.01800.

$\bullet $ Konstantin Ardakov and Peter Schneider. The Bernstein center in natural characteristic. arXiv e-prints, May 2021. arXiv:2105.06128.

$\bullet $ Rachel Ollivier and Peter Schneider. On the pro-$p$ Iwahori Hecke Ext-algebra of SL$_2(\mathbb Q_p)$. arXiv e-prints, April 2021. arXiv:2104.13422.

$\bullet $ Laurent Berger, Peter Schneider, and Bingyong Xie. Rigid character groups, Lubin-Tate theory, and $(\varphi ,\Gamma )$-modules. Mem. Amer. Math. Soc., 263(1275):v + 79, February 2020. doi:10.1090/memo/1275.

$\bullet $ Peter Schneider and Ernst-Wilhelm Zink. Zelevinsky operations for multisegments and a partial order on partitions. Pacific J. Math., 304(1):181–207, January 2020. doi:10.2140/pjm.2020.304.181.

$\bullet $ Rachel Ollivier and Peter Schneider. The modular pro-$p$ Iwahori-Hecke Ext-algebra. In Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan, and Erez M. Lapid, editors, Representations of Reductive Groups, volume 101 of Proceedings of Symposia in Pure Mathematics, pages 255–308. October 2019. doi:10.1090/pspum/101.

$\bullet $ Vladimir Berkovich, Walter Gubler, Peter Schneider, and Annette Werner. Non-Archimedean geometry and applications. Oberwolfach Rep., 16(1):513–575, February 2019. doi:10.4171/OWR/2019/8.