Tag Archives: Robert Coleman

More or less OPAQUE

I recently talked with Lynnelle Ye (a soon to be graduating student of Mark Kisin) for a few hours about her thesis and related mathematics. In her thesis, she generalizes (in part) the work Liu-Wan-Xiao on the boundary (halo) of … Continue reading

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Counting solutions to a_p = λ

We know that the eigenvalue of on is Are there any other level one cusp forms with the same Hecke eigenvalue? Maeda’s conjecture in its strongest form certainly implies that there does not. But what can one prove along these … Continue reading

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Chenevier on the Eigencurve

Today I wanted to mention a theorem of Chenever about components of the Eigencurve. Let denote weight space (which is basically a union of discs), and let be the Coleman-Mazur eigencurve together with its natural map to It will do … Continue reading

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Is Serre’s conjecture still open?

The conjecture in this paper has indeed been proven. But that isn’t the entire story. Serre was fully aware of Katz modular forms of weight one. However, Serre was too timid was prudently conservative and made his conjecture only for … Continue reading

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Robert Coleman

I was very sad to learn that, after a long illness with multiple sclerosis, Robert Coleman has just died. Robert’s influence on mathematics is certainly obvious to all of us in the field. Most of my personal interaction with him … Continue reading

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