Research Interests

Research Interests

$\bullet$ Arithmetic algebraic geometry, in particular the Langlands programme.
$\bullet$ $p$-adic Hodge theory and $p$-adic Galois representations.
$\bullet$ Automorphy of Galois representations.
$\bullet$ $p$-adic aspects of the theory of automorphic forms.

Selected Publications

Selected Publications of Prof. Dr. Eugen Hellmann

$\bullet$ C. Breuil, E. Hellmann, and B. Schraen. Une interprétation modulaire de la variété trianguline. Math. Ann., 367(3-4):1587–1645, 2017.

$\bullet$ C. Breuil, E. Hellmann, and B. Schraen. Smoothness and classicality on Eigenvarieties. Invent. Math., 209(1):197–274, 2017.

$\bullet$ E. Hellmann and B. Schraen. Density of potentially crystalline representations of fixed weight. Compos. Math., 152(8):1609–1647, 2016.

$\bullet$ E. Hellmann. Families of $p$-adic Galois representations and $(\varphi,\Gamma)$-modules. Comment. Math. Helv., 91(4):721–749, 2016.

$\bullet$ E. Hellmann. On arithmetic families of filtered $\phi$-modules and crystalline representations. J. Inst. Math. Jussieu, 12(4):677–726, 2013.

$\bullet$ E. Hellmann. The image of the coefficient space in the universal deformation space of a flat Galois representation of a $p$-adic field. Manuscripta Math., 139(3-4):273–290, 2012.

$\bullet$ E. Hellmann. On families of weakly admissible filtered $\phi$-modules and the adjoint quotient of ${\rm GL}_d$. Doc. Math., 16:969–991, 2011.

$\bullet$ E. Hellmann. Connectedness of Kisin varieties for ${\rm GL}_2$. Adv. Math., 228(1):219–240, 2011.

$\bullet$ E. Hellmann. On the structure of some moduli spaces of finite flat group schemes. Mosc. Math. J., 9(3):531–561, 2009.

Current Cluster Publications

Current Cluster Publications of Prof. Dr. Eugen Hellmann

$\bullet $ Eugen Hellmann. On the derived category of the Iwahori–Hecke algebra. Compositio Mathematica, 159(5):1042–1110, May 2023. doi:10.1112/S0010437X23007145.

$\bullet $ Matthew Emerton, Toby Gee, and Eugen Hellmann. An introduction to the categorical $p$-adic Langlands program. arXiv e-prints, October 2022. arXiv:2210.01404.

$\bullet $ Eugen Hellmann, Christophe M. Margerin, and Benjamin Schraen. Density of automorphic points in deformation rings of polarized global Galois representations. Duke Mathematical Journal, 171(13):2699–2752, January 2022. doi:10.1215/00127094-2021-0080.

$\bullet $ Urs Hartl and Eugen Hellmann. The universal family of semistable $p$-adic Galois representations. Algebra Number Theory, 14(5):1055–1121, July 2020. doi:10.2140/ant.2020.14.1055.

$\bullet $ Christophe Breuil, Eugen Hellmann, and Benjamin Schraen. A local model for the trianguline variety and applications. Publ. Math. IHES, 130(1):299–412, August 2019. doi:10.1007/s10240-019-00111-y.