Prof. Dr. Elmar Große-Klönne

Profil

Zusammenfassung

Prof. Große-Klönne ist Spezialist für p-adische Arithmetik und Darstellungstheorie, insbesondere für die Struktur von Modulformen, Hecke-Algebren und Kohomologietheorien über lokalen Körpern. Seine Expertise umfasst die Entwicklung von Methoden zur Analyse von arithmetischen Objekten mit p-adischen Techniken und deren Anwendung auf automorphe Formen und algebraische Strukturen.

Skills

Name

Prof. Dr. Elmar Große-Klönne

Titel

Prof. Dr.

Fakultät

Mathematisch-Naturwissenschaftliche Fakultät

Institut

Institut für Mathematik

Arbeitsgruppe

Algebra und Zahlentheorie

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HU-FIS-Profil

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Zuletzt gescrapt

28.6.2026, 01:05:57

• Arithmetik unendlichdimensionaler Lie Algebren

  Quelle ↗

  Zeitraum: 01/2012 - 12/2015 Projektleitung: Prof. Dr. Elmar Große-Klönne

• CENTRAL--06 Automorphische Techniken in Arithmetischer Geometrie

  Quelle ↗

  Förderer: DAAD Zeitraum: 03/2015 - 12/2018 Projektleitung: Prof. Dr. Elmar Große-Klönne

• Forschungaufenthalt Yuval Flicker, Ohio State Univ.

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  Förderer: Alexander von Humboldt-Stiftung Zeitraum: 06/2011 - 08/2011 Projektleitung: Prof. Dr. Elmar Große-Klönne

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• Frobenius and monodromy operators in rigid analysis, and Drinfel’d’s symmetric space

  2005

  Journal of Algebraic Geometry · 34 Zitationen · DOI

  We define Frobenius and monodromy operators on the de Rham cohomology of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -dagger spaces (rigid spaces with overconvergent structure sheaves) with strictly semistable reduction <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"> <mml:semantics> <mml:mi>Y</mml:mi> <mml:annotation encoding="application/x-tex">Y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , over a complete discrete valuation ring <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of mixed characteristic. For this we introduce log rigid cohomology and generalize the so-called Hyodo-Kato isomorphism to versions for non-proper <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"> <mml:semantics> <mml:mi>Y</mml:mi> <mml:annotation encoding="application/x-tex">Y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , for non-perfect residue fields, for non-integrally defined coefficients, and for the various strata of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"> <mml:semantics> <mml:mi>Y</mml:mi> <mml:annotation encoding="application/x-tex">Y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . We apply this to define and investigate crystalline structure elements on the de Rham cohomology of Drinfel’d’s symmetric space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and its quotients. Our results are used in a critical way in the recent proof of the monodromy-weight conjecture for quotients of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> given by de Shalit (2005).

• On special representations of p-adic reductive groups

  2014

  Duke Mathematical Journal · 21 Zitationen · DOI

  Let F be a non-Archimedean locally compact field, and let G be a split connected reductive group over F. For a parabolic subgroup Q⊂G and a ring L, we consider the G-representation on the L-module C∞(G/Q,L)/∑Q'⊋QC∞(G/Q',L).(∗) Let I⊂G denote an Iwahori subgroup. We define a certain free finite rank-L module M (depending on Q; if Q is a Borel subgroup, then (∗) is the Steinberg representation and M is of rank 1) and construct an I-equivariant embedding of (∗) into C∞(I,M). This allows the computation of the I-invariants in (∗). We then prove that if L is a field with characteristic equal to the residue characteristic of F and if G is a classical group, then the G-representation (∗) is irreducible. This is the analogue of a theorem of Casselman (which says the same for L=C); it had been conjectured by Vignéras. Herzig (for G=GLn(F)) and Abe (for general G) have given classification theorems for irreducible admissible modulo p representations of G in terms of supersingular representations. Some of their arguments rely on the present work.

• From pro-p Iwahori–Hecke modules to (φ,Γ)-modules, I

  2016

  Duke Mathematical Journal · 18 Zitationen · DOI

  Let o be the ring of integers in a finite extension K of Qp, and let k be its residue field. Let G be a split reductive group over Qp, and let T be a maximal split torus in G. Let H(G,I0) be the pro-p Iwahori–Hecke o-algebra. Given a semi-infinite reduced chamber gallery (alcove walk) C(•) in the T-stable apartment, a period ϕ∈N(T) of C(•) of length r, and a homomorphism τ:Zp×→T compatible with ϕ, we construct a functor from the category Modfin(H(G,I0)) of finite-length H(G,I0)-modules to étale (φr,Γ)-modules over Fontaine’s ring OE. If G=GLd+1(Qp), then there are essentially two choices of (C(•),ϕ,τ) with r=1, both leading to a functor from Modfin(H(G,I0)) to étale (φ,Γ)-modules and hence to GalQp-representations. Both induce a bijection between the set of absolutely simple supersingular H(G,I0)⊗ok-modules of dimension d+1 and the set of irreducible representations of GalQp over k of dimension d+1. We also compute these functors on modular reductions of tamely ramified locally unitary principal series representations of G over K. For d=1, we recover Colmez’s functor (when restricted to o-torsion GL2(Qp)-representations generated by their pro-p Iwahori invariants).

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