In the case of eigencurves, this completes the proof of Coleman-Mazur's `halo' conjecture.doi:10.1007/s00208-021-02184-9Ren, RufeiZhao, BinR. Ren, Spectral halo for Hilbert modular forms, in preparation.
The connective topological modular forms spectrum, tmftmf, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy...
In particular, we prove that on every irreducible component of Hilbert modular eigenvarieties, as a point moves towards the boundary, its \\(U_p\\) slope goes to zero. In the case of eigencurves, this completes the proof of Coleman鈥揗azur's 'halo' conjecture....
The local cohomology spectral sequence for topological modular formsJohn GreenleesJohn RognesRobert Bruner
M. Dickson, Local spectral equidistribution for degree 2 Siegel modular forms in level and weight aspects, Int. J. Number Theory 11 (2015), no. 2, 341-396.M. Dickson. Local spectral equidistribution for degree two Siegel modular forms in level and weight aspects. Int. J. Number Theory, ...
In the first case, it is shown that by running a summation over a finite orbit of the rational parameters, up to multiplication by the cusp form $\\\Delta$ of weight 12, each term $ilde a_{2n}$ lands in the 1-dimensional linear space of modular forms of weight 14. In the second...
doi:10.1090/surv/253Robert BrunerJohn RognesRobert Bruner and John Rognes, The adams spectral sequence for topological mod- ular forms. in preparation.Robert Bruner and John Rognes. The Adams spectral sequence for topological modular forms. In preparation....