Publications

62 results

On nearly holomorphic Drinfeld modular forms for admissible coefficient rings (2025)

arXiv preprint arXiv:2503.01357

Sriram Chinthalagiri Venkata

A duality result about special functions in Drinfeld modules of arbitrary rank (2025)

Res. Math. Sci.

Giacomo Ferraro

Bogomolov property for Galois representations with big local image (2025)

arXiv preprint arXiv:2503.14052

Joint with A. Conti, L. Terracini

On the Image of Automorphic Galois Representations (2025)

arXiv preprint arXiv:2502.10799

Alireza Shavali

$U$-Operators Acting on Harmonic Cocycles for $\mathrm{GL}_3$ and Their Slopes (2025)

arXiv preprint arXiv:2503.00141

Joint with G. Böckle, P. M. Gräf, T. Kaiser

Weak abelian direct summands and irreducibility of Galois representations (2024)

arXiv preprint arXiv:2404.08954, to appear in Mathematische Annalen

Joint with C.-Y. Hui

The trianguline variety for reductive groups and Zariski density of crystalline points (2024)

Preprint

Joint with A. Conti, J. Quast, M. Moakher

p-adic rigidity of eigenforms of infinite slope (2024)

arXiv preprint arXiv:2403.16918

Andrea Conti

Lifting Galois representations via Kummer flags (2024)

arXiv preprint arXiv:2403.08888

Joint with A. Conti, C. Demarche, M. Florence

Lattices in rigid analytic representations (2024)

arXiv preprint arXiv:2403.20232

Joint with A. Conti, E. Torti

On the Endomorphism Algebra of Abelian Varieties Associated with Hilbert Modular Forms (2024)

arXiv preprint arXiv:2410.20223

Alireza Shavali

Local constancy of families of Galois representations modulo prime powers (2023)

Preprint

Joint with A. Conti, E. Torti

L-invariants and deep congruences between newforms (2023)

Preprint

Joint with A. Conti, P. Graef

Big images of two-dimensional pseudorepresentations (2023)

Mathematische Annalen, Vol. 385 (3-4), pp. 1085-1179 (2023), arXiv:1904.10519

Joint with A. Conti, J. Lang, A. Medvedovsky

Equidimensionality of universal pseudodeformation rings in characteristic p for absolute Galois groups of p-adic fields (pdf), 91 pages. (2023)

Forum of Mathematics, Sigma, Vol. 11:e102

Joint with A.-K. Juschka

A class of functional identities associated to curves over finite fields (2022)

Preprint

Giacomo Ferraro

A Hecke-equivariant decomposition of spaces of Drinfeld cusp forms via representation theory, and an investigation of its subfactors (2021)

arXiv preprint arXiv:2103.13126

Joint with P. M. Gräf, R. Perkins

Deformation rings and images of Galois representations (2021)

arXiv preprint arXiv:2107.03114, to appear

Joint with S. Arias-de-Reyna

Lifting trianguline Galois representations along isogenies (2021)

arXiv preprint arXiv:2101.02189

Andrea Conti

Magma package to compute Hecke eigensystems for harmonic cocycles on the Bruhat-Tits tree for GL_2(F_q(T)) by Master's student Burak Cakir, thesis available here. (2020)

Workshop Arithmetic Geometry and Computer Algebra (2020)

Gebhard Böckle

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

Slides for the Journées du GDR TLAG 2021 (Rennes, 24/03/2021 - 26/03/2021) (2020)

Gebhard Böckle

Boundary Distributions for GL3 over a Local Field and Symmetric Power Coefficients (Ph.D. thesis, 2020, pdf) (2020)

Gebhard Böckle

published version (2) (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)

Notes from a Lecture Series at the CRM Barcelona, Spring 2010

Gebhard Böckle

Algebraic Hecke characters and compatible systems of abelian mod p Galois representations over global fields. (2020)

Manuscripta Math.

Gebhard Böckle

Independence of l-adic representations of geometric Galois groups. (2020)

J. Reine Angew. Math., arXiv:1302.6597

Joint with W. Gajda, S. Petersen

Irreducibility of versal deformation rings in the (p,p)-case for 2-dimensional representations. (2020)

J. Algebra

Joint with A.-K. Juschka

New Bounds on the Biplanar and $k$-Planar Crossing Numbers (2019)

CCCG 2022

Joint with A. Shavali, H. Zarrabi-Zadeh

$\hat G$-local systems on smooth projective curves are potentially automorphic (2019)

Published

Joint with G. Böckle, M. Harris, C. Khare, J. A. Thorne

Hecke characters associated to Drinfeld modular forms (2015)

Compositio Mathematica, Vol. 151(2015), pp. 2437-2477

Gebhard Böckle

Computations with Modular Forms (2014)

Joint with G. Wiese

Galois representations (2013)

Travaux mathématiques.

Gebhard Böckle

The distribution of the zeros of the Goss zeta-function for A=F2[x,y]/(y2+y+x3+x+1) (2013)

Math. Z.

Gebhard Böckle

Cartier Crystals. An overview can be found in a chapter of the habilitation treatise of M.Blickle (2013)

arXiv preprint arXiv:1309.1035

Joint with M. Blickle

Cohomological theory of crystals over function fields and applications (2012)

In "Arithmetic Geometry in Positive Characteristic". Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser Verlag, Basel (2012), to appear.

Gebhard Böckle

On computing quaternion quotient graphs for function fields. (2012)

J. Théor. Nombres Bordeaux, Vol. 24(1), pp. 73-99, arXiv:1010.4826

Joint with R. Butenuth

Cartier Modules: finiteness results (2011)

J. Reine Angew. Math. 661 (2011), 85-123

Joint with M. Blickle

Deformation rings for some mod 3 Galois representations of the absolute Galois group of Q3 (2010)

Astérisque 330 (2010), pp. 529-542

Gebhard Böckle

Cohomological Theory of Crystals over Function Fields Tracts in Mathematics 5, European Mathematical Society (2009)

Tracts in Mathematics 5, European Mathematical Society (2009).

Joint with R. Pink

The Miller-Rabin test with randomized exponents (2009)

J. Math. Cryptol.

Gebhard Böckle

Deformations and the rigidity method (2008)

J. Algebra 320 (2008), 3613-3658

Gebhard Böckle

Uniformizable families of t-motives (2007)

Trans. Amer. Math. Soc.

Joint with U. Hartl

Presentations of universal deformation rings (2007)

in: $L$-functions and Galois representations, 24--58, LMS Lecture Note Ser., 320, Cambridge Univ. Press, Cambridge (2007).

Gebhard Böckle

Mod l representations of arithmetic fundamental groups. II. A conjecture of A. J. de Jong (2006)

Compos. Math.

Joint with C. Khare

Arithmetic over function fields: a cohomological approach (2005)

Number fields and function fields---two parallel worlds,

Gebhard Böckle

Mod l representations of arithmetic fundamental groups. I. An analog of Serre's conjecture for function fields (2005)

Duke Math. J.

Joint with C. Khare

On the isomorphism R0 -> T0 (2003)

appendix to

Gebhard Böckle

Lifting mod p representations to characteristic p2 (2003)

J. Number Theory

Gebhard Böckle

Global L-functions over function fields (2002)

Math. Ann.

Gebhard Böckle

Finiteness conjectures for Fl[[T]]-analytic extensions of number fields (2002)

J. Number Theory

Gebhard Böckle

An Eichler-Shimura isomorphism over function fields between Drinfeld modular forms and cohomology classes of crystals. (pdf), 183 pages. (2002)

Preprint, 183 pages

Gebhard Böckle

A remark on a finiteness conjecture on mod $p$ Galois representations by C. Khare (2001)

J. Ramanujan Math. Soc.

Gebhard Böckle

On the density of modular points in universal deformation spaces (2001)

Amer. J. Math.

Gebhard Böckle

Demuskin groups with group actions and applications to deformations of Galois representations (2000)

Compositio Math.

Gebhard Böckle

Explicit universal deformations of even Galois representations (1999)

Math. Nachr.

Gebhard Böckle

A local-to-global principle for deformations of Galois representations (1999)

J. Reine Angew. Math.

Gebhard Böckle

The prime-to-adjoint principle and unobstructed Galois deformations in the Borel case (1999)

J. Number Theory

Joint with A. Mezard

The generic fiber of the universal deformation space associated to a tame Galois representation (1998)

Manuscripta Math.

Gebhard Böckle

Software Packages

Magma package QaQuotGraphs

to compute the action by unit groups of maximal orders in quaternion algebras over $F_q(T)$.

By Dr. Ralf Butenuth

Magma package (Bruhat-Tits buildings)

to compute quotients of Bruhat-Tits buildings over function fields modulo congruence subgroups and the action of Hecke operators on harmonic cocycles with coefficients in char. 0.

By Lutz Hofmann

Magma package (Hecke eigensystems)

to compute Hecke eigensystems for harmonic cocycles on the Bruhat-Tits tree for $GL_2(F_q(T))$, thesis available here.

By Burak Cakir