Prof. Dr. Gebhard Böckle
Group Leader
Biography
Gebhard Böckle is Professor of Mathematics and head of the Arithmetic Geometry research group at Heidelberg University. Born in 1964 in Herrenberg, Germany, he completed his PhD at the University of Illinois at Urbana-Champaign. His research focuses on Galois representations over number and function fields, the arithmetic of automorphic forms over function fields, cohomology of arithmetic groups, and the p-adic Langlands program. He has supervised numerous PhD students and postdocs, making significant contributions to algebraic number theory and arithmetic geometry.
Research Interests
Galois representations over number and function fields, arithmetic of automorphic forms over function fields, cohomology of arithmetic groups, Drinfeld modular varieties, p-adic Langlands program, deformations of Galois representations, eigenvarieties over adic spaces
Publications
$U$-Operators Acting on Harmonic Cocycles for $\mathrm{GL}_3$ and Their Slopes (2025)
arXiv preprint arXiv:2503.00141
Slides for the Special Session on Drinfeld Modules, Modular Varieties and Arithmetic Applications (AMS Fall Eastern Virtual Sectional Meeting, 03/10/2020 - 04/10/2020) (2020)
Gebhard Böckle
Boundary Distributions for GL3 over a Local Field and Symmetric Power Coefficients (Ph.D. thesis, 2020, pdf) (2020)
Gebhard Böckle
Computing L-invariants via the Greenberg-Stevens formula (2020)
Joint with S. Anni, G. Böckle, A. Troya, Journal de Théorie des Nombres de Bordeaux 31, 727–746, 2019, published version
published version (2020)
Joint with G. Böckle, R. Perkins, Research in Number Theory 7, Article number: 44, 2021, published version
Deformations of Galois representations (2020)
Gebhard Böckle
Notes from a Lecture Series at the CRM Barcelona, Spring 2010
Algebraic Hecke characters and compatible systems of abelian mod p Galois representations over global fields. (2020)
Gebhard Böckle
Manuscripta Math.
$\hat G$-local systems on smooth projective curves are potentially automorphic (2019)
Joint with G. Böckle, M. Harris, C. Khare, J. A. Thorne
Published
Hecke characters associated to Drinfeld modular forms (2015)
Gebhard Böckle
Compositio Mathematica, Vol. 151(2015), pp. 2437-2477
The distribution of the zeros of the Goss zeta-function for A=F2[x,y]/(y2+y+x3+x+1) (2013)
Gebhard Böckle
Math. Z.
Cohomological theory of crystals over function fields and applications (2012)
Gebhard Böckle
In "Arithmetic Geometry in Positive Characteristic". Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser Verlag, Basel (2012), to appear.
Deformation rings for some mod 3 Galois representations of the absolute Galois group of Q3 (2010)
Gebhard Böckle
Astérisque 330 (2010), pp. 529-542
Presentations of universal deformation rings (2007)
Gebhard Böckle
in: $L$-functions and Galois representations, 24--58, LMS Lecture Note Ser., 320, Cambridge Univ. Press, Cambridge (2007).
Arithmetic over function fields: a cohomological approach (2005)
Gebhard Böckle
Number fields and function fields---two parallel worlds,
Finiteness conjectures for Fl[[T]]-analytic extensions of number fields (2002)
Gebhard Böckle
J. Number Theory
An Eichler-Shimura isomorphism over function fields between Drinfeld modular forms and cohomology classes of crystals. (pdf), 183 pages. (2002)
Gebhard Böckle
Preprint, 183 pages
A remark on a finiteness conjecture on mod $p$ Galois representations by C. Khare (2001)
Gebhard Böckle
J. Ramanujan Math. Soc.
On the density of modular points in universal deformation spaces (2001)
Gebhard Böckle
Amer. J. Math.
Demuskin groups with group actions and applications to deformations of Galois representations (2000)
Gebhard Böckle
Compositio Math.
A local-to-global principle for deformations of Galois representations (1999)
Gebhard Böckle
J. Reine Angew. Math.
The generic fiber of the universal deformation space associated to a tame Galois representation (1998)
Gebhard Böckle
Manuscripta Math.
Teaching
Seminar on Homological Algebra (Summer 2025)
Seminar
Hauptseminar Arithmetik von Zahl- und Funktionenkörpern: Congruence Modules and the Wiles–Lenstra–Diamond Numerical Criterion in Higher Codimension (Winter 2024)
Seminar
Seminar on Commutative Algebra (Winter 2024)
Seminar
Vorlesung Modularity and Galois Representations (Winter 2024)
Lecture
Hauptseminar Arithmetik von Zahl- und Funktionenkörpern: Shtukas for reductive groups and global Langlands correspondence after Vincent Lafforgue (Summer 2024)
Seminar
Seminar on Representation theory of finite groups (Summer 2024)
Seminar
Vorlesung Algebra 2 (Summer 2024)
Lecture
Hauptseminar Arithmetik von Zahl- und Funktionenkörpern: Rigid meromorphic cocycles (Winter 2023)
Seminar
Proseminar on Quadratic forms (Winter 2023)
Seminar
Vorlesung Algebra 1 (Winter 2023)
Lecture
Hauptseminar Arithmetik von Zahl- und Funktionenkörpern: Vectorial Drinfeld modular forms over Tate algebras (Summer 2023)
Seminar
Proseminar p-adic numbers (Summer 2023)
Seminar
Vorlesung Lineare Algebra 2 (Summer 2023)
Lecture
Seminar on Affine Algebraic Groups (Winter 2022)
Seminar
Magma package to compute Hecke eigensystems for harmonic cocycles on the Bruhat-Tits tree for $GL_2(F_q(T))$
Vorlesung Lineare Algebra 1 (Winter 2022)
Lecture
Hauptseminar Arithmetik von Zahl- und Funktionenkörpern: Plectic Stark-Heegner points (Winter 2021)
Seminar
Seminar Abelian Varieties (Winter 2021)
Seminar
Vorlesung Étale Kohomologie (Winter 2021)
Lecture
Seminar Derivierte Kategorien und Algebraische Geometrie (Summer 2021)
Seminar
Vorlesung Algebraische Geometrie 2 (Summer 2021)
Lecture
Seminar Elliptische Kurven (Winter 2020)
Seminar
Vorlesung Algebraische Geometrie 1 (Winter 2020)
Lecture
Vorlesung Algebra 2 (Summer 2020)
Lecture
Algebra 1 (Winter 2019)
Lecture
Hauptseminar: Arithmetik von Zahl- und Funktionenkörpern (Winter 2019)
Seminar
Seminar: Affine algebraische Gruppen (Winter 2019)
Seminar
Hauptseminar: Arithmetik von Zahl- und Funktionenkörpern (Summer 2019)
Seminar
Kompatible Systeme von Galoisdarstellungen (Summer 2019)
Lecture
Proseminar: Bilinearformen und klassische Gruppen (Summer 2019)
Proseminar
Galoiskohomologie und Galoisdarstellungen (Winter 2018)
Lecture
Hauptseminar: Arithmetik von Zahl- und Funktionenkörpern (Winter 2018)
Seminar
Seminar: Darstellungstheorie von GL_2 (Winter 2018)
Seminar
Algebraische Zahlentheorie 2 (Summer 2018)
Lecture
Hauptseminar: Arithmetik von Zahl- und Funktionenkörpern (Summer 2018)
Seminar
Seminar: Lokale Klassenkörpertheorie nach Lubin-Tate (Summer 2018)
Seminar
Algebraische Zahlentheorie 1 (Winter 2017)
Lecture
Hauptseminar: Arithmetik von Zahl- und Funktionenkörpern (Winter 2017)
Seminar
Seminar: Gruppenkohomologie (Winter 2017)
Seminar
Hauptseminar: Arithmetik von Zahl- und Funktionenkörpern (Winter 2016)
Seminar
Proseminar: Primzahlen und Faktorisierung für die Kryptographie (Winter 2016)
Proseminar
Lineare Algebra 1 (Winter 2016)
Lecture
Hauptseminar: Arithmetik von Zahl- und Funktionenkörpern (Summer 2016)
Seminar
Lineare Algebra 2 (Summer 2016)
Lecture
Proseminar: p-adische Analysis (Summer 2016)
Proseminar
Hauptseminar Arithmetik von Zahl- und Funktionenkörpern: "Lenny Taelman´s body of work on Drinfeld modules" (Summer 2015)
Seminar
Seminar "Darstellungstheorie" (Summer 2015)
Seminar
Vorlesung "Bruhat-Tits Gebäude" (Summer 2015)
Lecture
Hauptseminar Arithmetik von Zahl- und Funktionenkörpern: "Recent results towards the BSD conjecture for elliptic curves over Q" (Winter 2014)
Seminar
Seminar "Klassenkörpertheorie über Funktionenkörpern und Drinfeld Moduln" (Winter 2014)
Seminar
Vorlesung "Automorphe Formen" (Winter 2014)
Lecture
Hauptseminar "Arithmetik von Zahl- und Funktionenkörpern: Shimura Varieties" (Summer 2014)
Seminar
Seminar "p-adische Geometrie" (Summer 2014)
Seminar
Spezialvorlesung "Abelsche Varietäten II" (Summer 2014)
Lecture
Vorlesung "Algebraische Gruppen" (Summer 2014)
Lecture
Abelsche Varietäten I (Winter 2013)
Lecture
Arithmetik von Zahl- und Funktionenkörpern: "Modularity Lifting" (Winter 2013)
Seminar
Seminar "Deformationen von (Pseudo-)Darstellungen" (Winter 2013)
Seminar
Étale Kohomologie (Winter 2013)
Lecture
Algebraische Geometrie 2 (Summer 2013)
Lecture
Seminar "Torische Varietäten" (Summer 2013)
Seminar
Seminar "Trianguline Representations" (Summer 2013)
Seminar
Algebraische Geometrie 1 (Winter 2012)
Lecture
Seminar "Affine algebraische Gruppen" (Winter 2012)
Seminar
Seminar "Transcendence theory in positive characteristic" (Winter 2012)
Seminar
Algebra 1 (Winter 2011)
Lecture
Proseminar "Bilinear forms and classical groups" (Winter 2011)
Seminar
Seminar "Borcherds Products" (Winter 2011)
Seminar
Algebraic groups and buildings (Winter 2010)
Lecture
Linear Algebra 1 (Winter 2010)
Lecture
Seminar "Hecke operators and their algorithmic" (Winter 2010)
Seminar
Arbeitsgemeinschaft: Study group on p-adic L-functions and the Mazur-Tate-Teitelbaum conjecture (Summer 2009)
Seminar
Mathematik für Biologen (Summer 2009)
Lecture
Anwendungsoriente Algebra und Zahlentheorie (Winter 2008)
Lecture
Arbeitsgemeinschaft: p-adische Galoisdarstellungen (Winter 2008)
Seminar
Riemannsche Flächen 1 (Winter 2008)
Lecture
Arbeitsgemeinschaft: Eine kanonische Kompaktifizierung des Modulraums Abelscher Varietäten (Summer 2008)
Seminar
Arbeitsgemeinschaft: Quaternionenalgebren (Summer 2008)
Seminar
Explizite Klassenkörpertheorie (Summer 2008)
Lecture
Seminar "Quadratische Formen" (Summer 2008)
Seminar
Arbeitsgemeinschaft: Kolyvagin's Euler system for elliptic curves (Winter 2007)
Seminar
Algebraische Zahlentheorie 2 (Summer 2007)
Lecture
Arbeitsgemeinschaft: Einführung in die Theorie der Automorphen Formen (Summer 2007)
Seminar
Seminar "Elliptische Kurven" (Summer 2007)
Seminar
Algebraische Zahlentheorie 1 (Winter 2006)
Lecture
Seminar "Homologische Algebra" (Winter 2006)
Seminar
Algebra 2 (Summer 2006)
Lecture
Arbeitsgemeinschaft: Über eine Vermutung von A.J. de Jong (Summer 2006)
Seminar
Proseminar "Zahlentheorie" (Summer 2006)
Seminar
Algebra 1 (Winter 2005)
Lecture
Arbeitsgemeinschaft: Galoisdarstellungen zu Modulformen (Winter 2005)
Seminar
Proseminar "Aspekte zum Thema Zahlen" (Winter 2005)
Seminar
Arbeitsgemeinschaft: Hilbertsche Modulformen (Summer 2005)
Seminar
Lineare Algebra 2 (Summer 2005)
Lecture
Arithmetik von Modulformen (Winter 2004)
Lecture
Lineare Algebra 1 (Winter 2004)
Lecture
Arbeitsgemeinschaft: Klassenkörpertheorie (Summer 2004)
Seminar
Drinfeld Moduln (Summer 2004)
Lecture
Seminar "Elementare Algorithmen in der Zahlentheorie" (Summer 2004)
Seminar
Anwendungsorientierte Zahlentheorie und Algebra (Winter 2003)
Lecture
Schwerpunktseminar Zahlentheorie: Pointcounting over finite fields (Winter 2003)
Seminar
Elliptische Kurven und Anwendungen in der Krytographie (Summer 2003)
Lecture