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Mathematics Münster

A: Arithmetic and Groups

A1: Arithmetic, geometry and representations
Current PublicationsNguyen, Kieu Hieu; Viehmann, Eva A Harder-Narasimhan stratification of the B_{dR}^+-Grassmannian. Compositio Mathematica Vol. 159 (4), 2023 online
Viehmann, Eva On Newton strata in the B_{dR}^+-Grassmannian.. Duke Mathematical Journal Vol. 173 (1), 2023 online
Viehmann, Eva Minimal Newton strata in Iwahori double cosets. International Mathematics Research Notices Vol. 2019 (7), 2021, pp 5349-5365 online
U. Hartl, E. Viehmann The generic fiber of moduli spaces of bounded local G-shtukas. Journal of the Institute of Mathematics of Jussieu Vol. 2021, 2021, pp 1-80 online
Trentin S., Viehmann E. Closure relations of Newton strata in Iwahori double cosets. Manuscripta Mathematica Vol. 2021, 2021 online
Hamacher P, Viehmann E Finiteness properties of affine Deligne-Lusztig varieties. Documenta Mathematica Vol. 25, 2020, pp 899-910 online
Milićević E, Viehmann E Generic Newton points and the Newton poset in Iwahori-double cosets. Forum of Mathematics, Sigma Vol. 8, 2020, pp Paper No. e50, 18 online
Viehmann, Eva On the geometry of the Newton stratification. Stabilization of the trace formula, Shimure varieties, and arithmetic applications, Volume II: Shimura varieties and Galois representationsLondon Mathematical Society Lecture Notes, 2020 online
Chen M, Viehmann E Affine Deligne-Lusztig varieties and the action of {$J$}. Journal of Algebraic Geometry Vol. 27 (2), 2018, pp 273-304 online
Current ProjectsCRC 1442: Geometry: Deformation and Rigidity - A05: Moduli spaces of local shtukas in mixed characteristic

We study the geometry and cohomology of moduli spaces of local G-shtukas, a class of moduli spaces that plays a central role in the geometrisation of Langlands correspondences. More precisely, we are interested in the geometry of the image of the period maps, want to investigate étale sheaves on the moduli spaces and aim at the local Langlands correspondence for covering groups via a metaplectic geometric Satake equivalence.

Geometry and Arithmetic of Uniformized Structures online
EXC 2044 - A1: Arithmetic, geometry and representations The Langlands programme relates representations of (the adele valued points of) reductive groups G over Q - so-called automorphic representations - with certain representations of the absolute Galois group of Q. This programme includes the study of these objects over general global fields (finite extension of Q or Fp (t)) and local fields as well. In its local form the classical programme onlyconsidered l-adic Galois representations of p-adic fields for unequal primes l neq p. In order to allow for a p-adic variation of the objects, it is absolutely crucial to extend it to the case l = p. In the global situation, the automorphic representations in question can often be realised in (or studied via) the cohomology of a tower of Shimura varieties (or related moduli spaces) attached to the group G. We will focus on the following directions within this programme: The p-adic and mod p Langlands programme asks for an extension of such a correspondence involving certain continuous representations with p-adic respectively mod p coefficients. Broadening the perspective to p-adic automorphic forms should, for example, enable us to capture all Galois representations, not just those having a particular Hodge theoretic behaviour at primes dividing p. This extended programme requires the introduction of derived categories. We will study differential graded Hecke algebras and their derived categories on the reductive group side. On the Galois side, we hope to use derived versions of the moduli spaces of p-adic Galois representations introduced by Emerton and Gee. The geometric Langlands programme is a categorification of the Langlands programme. We plan to unify the different approaches using motivic methods. In another direction, we study the geometry and arithmetic of moduli stacks of global G-shtukas over function fields. Their cohomology has been the crucial tool to establish large parts of the local and global Langlands programme over function fields. Variants of G-shtukas are also used to construct and investigate families of p-adic Galois representations.

Cohomology theories are a universal tool pervading large parts of algebraic and arithmetic geometry. We will develop and study cohomology theories, especially in mixed characteristic, that generalise and unify étale cohomology, crystalline cohomology and de Rham cohomology as well as Hochschild cohomology in the non-commutative setting. Developing (topological) cyclic homology in new contexts is an important aim. A main goal is to construct a cohomology theory that can serve the same purposes for arithmetic schemes as the l-adic or crystalline cohomology with their Frobenius actions for varieties over finite fields. Ideas from algebraic geometry, algebraic topology, operator algebras and analysis blend in these investigations. online
Phone+49 251 83-33701
FAX+49 251 83-33786
Secretary   Sekretariat Harenbrock/Reckermann
Frau Ina Reckermann
Telefon +49 251 83-33700
Fax +49 251 83-33786
Zimmer 316
AddressProf. Dr. Eva Viehmann
Mathematisches Institut
Fachbereich Mathematik und Informatik der Universität Münster
Einsteinstrasse 62
48149 Münster
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