Publications and Preprints

of Prof. Dr. Gebhard Böckle

Research articles

• (joint with A.-K. Juschka) Irreducibility of versal deformation rings in the (p,p)-case for 2-dimensional representations. (pdf)
  J. Algebra 444 (2015), 81–123.
• (joint with W. Gajda, S. Petersen) Independence of l-adic representations of geometric Galois groups. (pdf)
  J. Reine Angew. Math. (2015), 25 p.
• Hecke characters associated to Drinfeld modular forms (Appendix B joint with T. Centeleghe). (pdf)
  Compos. Math. (2015), 53 p.
• The distribution of the zeros of the Goss zeta-function for A=F₂[x,y]/(y²+y+x³+x+1). (pdf)
  Math. Z. 275 (2013), no. 3-4, 835–861.
• Algebraic Hecke characters and compatible systems of abelian mod p Galois representations over global fields. (pdf)
  Manuscripta Math. 140 (2013), no. 3-4, 303-331.
• (joint with R. Butenuth) On computing quaternion quotient graphs for function fields. (pdf)
  J. Théor. Nombres Bordeaux 24 (2012), no. 1, 73-99.
• (joint with M. Blickle) Cartier Modules: finiteness results. (pdf)
  J. Reine Angew. Math. 661 (2011), 85-123
• Deformation rings for some mod 3 Galois representations of the absolute Galois group of Q₃ (pdf)
  in Representations p-adic de groupes p-adiques II: Representations de GL₂(Q_p) et (φ,Γ)-modules, ed. L.Berger, C. Breuil, P. Colmez, Asterisque 330 (2010), 529-542
• The Miller-Rabin test with randomized exponents. (pdf)
  J. Math. Cryptol. 3 (2009), no. 4, 307-319
• Deformations and the rigidity method (pdf)
  J. Algebra 320 (2008), no. 10, 3613-3658
• Presentations of universal deformation rings. (pdf)
  in: $L$-functions and Galois representations, 24--58, LMS Lecture Note Ser., 320, Cambridge Univ. Press, Cambridge  (2007).
• (joint with U. Hartl) Uniformizable families of t-motives. (pdf)
  Trans. Amer. Math. Soc. 359 (2007), no. 8, 3933-3972.
• (joint with C. Khare) Mod l representations of arithmetic fundamental groups. II. A conjecture of A. J. de Jong. (pdf)
  Compos. Math. 142 (2006), no. 2, 271-294.
• (joint with C. Khare) Mod l representations of arithmetic fundamental groups. I. An analog of Serre's conjecture for function fields. (pdf)
  Duke Math. J. 129 (2005), no. 2, 337-369.
• Arithmetic over function fields: a cohomological approach. (pdf)
  Number fields and function fields---two parallel worlds, 1--38, Progr. Math., 239, Birkhäuser Boston, Boston, MA (2005).
• Lifting mod p representations to characteristic p². (pdf)
  J. Number Theory 101 (2003), no. 2, 310-337.
• On the isomorphism R₀ -> T₀. (pdf)
  appendix to On isomorphisms between deformation and Hecke rings by C. Khare.
  Inventiones Math. 154 (2003), no. 1, 217-222.
• Finiteness conjectures for F_l[[T]]-analytic extensions of number fields. (pdf)
  J. Number Theory 96 (2002), no. 2, 257-274.
• Global L-functions over function fields. (pdf)
  Math. Ann. 323 (2002), no. 4, 737-795.
• On the density of modular points in universal deformation spaces. (pdf)
  Amer. J. Math. 123 (2001), no. 5, 985-1007.
• A remark on a finiteness conjecture on mod $p$ Galois representations by C. Khare. (pdf)
  J. Ramanujan Math. Soc. 16 (2001), no. 1, 39-44.
• Demuskin groups with group actions and applications to deformations of Galois representations. (pdf)
  Compositio Math. 121 (2000), no. 2, 109-154.
• (joint with A. Mezard) The prime-to-adjoint principle and unobstructed Galois deformations in the Borel case. (pdf)
  J. Number Theory 78 (1999), no. 2, 167-203.
• A local-to-global principle for deformations of Galois representations. (pdf)
  J. Reine Angew. Math. 509 (1999), 199-236.
• Explicit universal deformations of even Galois representations. (pdf)
  Math. Nachr. 206 (1999), 85-110.
• The generic fiber of the universal deformation space associated to a tame Galois representation. (pdf)
  Manuscripta Math. 96 (1998), no. 2, 231-246.

Lecture Series and Surveys

• Deformations of Galois representations. (pdf)
  In Elliptic curves, Hilbert modular forms and Galois deformations, 21–115, Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser/Springer, Basel (2013).
• Cohomological theory of crystals over function fields and applications. (pdf)
  In "Arithmetic Geometry in Positive Characteristic". Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser Verlag, Basel (2012), to appear.
• Galois representations. (pdf)
  Travaux mathématiques. Vol. XXIII, 5–35, Fac. Sci. Technol. Commun. Univ. Luxemb., Luxembourg (2013).

Books

• (joint with G. Wiese): Computations with Modular Forms (2014).
• (joint with R. Pink) Cohomological Theory of Crystals over Function Fields
  Tracts in Mathematics 5, European Mathematical Society (2009).

Preprints

• (joint with A.-K. Juschka) Equidimensionality of universal pseudodeformation rings in characteristic p for absolute Galois groups of p-adic fields (pdf), 91 pages.
• An Eichler-Shimura isomorphism over function fields between Drinfeld modular forms and cohomology classes of crystals. (pdf), 183 pages.

In Preparation

• (joint with M. Blickle) Cartier Crystals. An overview can be found in a chapter of the habilitation treatise of M.Blickle
• (joint with M. Dettweiler) Division Towers for Triangle Shimura Curves.
• Lifts of mod p Galois representations with local supercuspidal types.