References of "Dimitrov, Mladen"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailL-invariants of Artin motives
Dimitrov, Mladen; Maksoud, Alexandre UL

in Annales mathématiques du Québec (2022)

We compute Benois L-invariants of weight 1 cuspforms and of their adjoint representations and show how this extends Gross’ p-adic regulator to Artin motives which are not critical in the sense of Deligne ... [more ▼]

We compute Benois L-invariants of weight 1 cuspforms and of their adjoint representations and show how this extends Gross’ p-adic regulator to Artin motives which are not critical in the sense of Deligne. Benois’ construction depends on the choice of a regular submodule which is well understood when the representation is p-regular, as it then amounts to the choice of a “motivic” p-refinement. The situation is dramatically different in the p-irregular case, where the regular submodules are parametrized by a flag variety and thus depend on continuous parameters. We are nevertheless able to show in some examples, how Hida theory and the geometry of the eigencurve can be used to detect a finite number of choices of arithmetic and “mixed-motivic” significance. [less ▲]

Detailed reference viewed: 15 (0 UL)
Full Text
Peer Reviewed
See detailUnramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod p
Dimitrov, Mladen; Wiese, Gabor UL

in Journal of the Institute of Mathematics of Jussieu (2020), 19(2), 281-306

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This ... [more ▼]

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight 1. The proof is based on the observation that parallel weight 1 forms in characteristic p embed into the ordinary part of parallel weight p forms in two different ways per prime dividing p, namely via `partial' Frobenius operators. MSC: 11F80 (primary); 11F41, 11F33 Keywords: Hilbert modular forms modulo p, weight one, Galois representations [less ▲]

Detailed reference viewed: 106 (5 UL)
Full Text
See detailUnramifiedness of weight one Hilbert Hecke algebras
Deo, Shaunak; Dimitrov, Mladen; Wiese, Gabor UL

E-print/Working paper (2019)

We prove that the Galois pseudo-representation valued in the mod p^n parallel weight 1 Hecke algebra for GL(2) over a totally real number field F is unramified at a place above p if p-1 does not divide ... [more ▼]

We prove that the Galois pseudo-representation valued in the mod p^n parallel weight 1 Hecke algebra for GL(2) over a totally real number field F is unramified at a place above p if p-1 does not divide the ramification index at that place. A novel geometric ingredient is the construction and study, in the case when p ramifies in F, of generalised Theta-operators using Reduzzi-Xiao's generalised Hasse invariants, including especially an injectivity criterion in terms of minimal weights. [less ▲]

Detailed reference viewed: 69 (5 UL)