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Newton polygons of Hecke operators
In this computational paper we verify a truncated version of the Buzzard–Calegari conjecture on the Newton polygon of the Hecke operator
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The Fargues-Fontaine Curve and p-Adic Hodge Theory
This survey paper is based, in part, on the author’s lectures at the summer school that was held at Tata Institute’s ICTS in Bangalore in August...
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Harmonic Maass form eigencurves
We construct two families of harmonic Maass Hecke eigenforms. Using these families, we construct p -adic harmonic Maass forms in the sense of Serre....
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An Introduction to p-Adic Hodge Theory
These notes provide an introduction to p-adic Hodge theory. They are based on the series of lectures given by the author at the International Center...
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A trace formula approach to control theorems for overconvergent automorphic forms
We present an approach to proving control theorems for overconvergent automorphic forms on Harris–Taylor unitary Shimura varieties based on a...
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A quaternionic construction of p-adic singular moduli
Rigid meromorphic cocycles were introduced by Darmon and Vonk as a conjectural p -adic extension of the theory of singular moduli to real quadratic...
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Derivatives of Frobenius and Derivatives of Hodge—Tate Weights
In this paper we study the derivatives of Frobenius and the derivatives of Hodge—Tate weights for families of Galois representations with...
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Triple product p-adic L-functions for balanced weights
We construct p -adic triple product L -functions that interpolate (square roots of) central critical L -values in the balanced region. Thus, our...
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A 0.5 (half) overconvergent Eichler-Shimura isomorphism
In this article we construct a Galois and Hecke equivariant morphism connecting the first cohomology group on Faltings’ site of a formal strict...
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A local model for the trianguline variety and applications
We describe the completed local rings of the trianguline variety at certain points of integral weights in terms of completed local rings of algebraic...
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The adic, cuspidal, Hilbert eigenvarieties
We construct adic, compactified eigenvarieties parameterizing adic overconvergent Hilbert modular eigenforms of finite slope by constructing integral...
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Slopes of Modular Forms
We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first...
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p-adic families of modular forms and p-adic Abel-Jacobi maps
We show that p -adic families of modular forms give rise to certain p -adic Abel-Jacobi maps at their p -new specializations. We introduce the concept...
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Rankin–Eisenstein classes in Coleman families
We show that the Euler system associated with Rankin–Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings,...
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Gross–Stark units and p-adic iterated integrals attached to modular forms of weight one
This article can be read as a companion and sequel to the authors’ earlier article on Stark points and p -adic iterated integrals attached to modular...
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On the regulator formulas of Bertolini, Darmon and Rotger
We give a unified, and somewhat simplified, account of the regulator formulas appearing in papers of Bertolini, Darmon and Rotger, describing the...