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On the variation of slopes over moduli stacks of Galois representations

John Bergdall, Robert Pollack

Source record

Source: arXiv

Published: Sep 10, 2026

arXiv: 2609.12281

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Source abstract

We determine how p-adic slopes of modular forms vary as their associated Galois representations modulo p vary over moduli of Galois representations. As a consequence, we show that the authors' ghost conjecture recently proven by Liu, Truong, Xiao, and Zhao is "stable under direct sums".

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On the variation of slopes over moduli stacks of Galois representations — Mathematical Frontier Network