On the variation of slopes over moduli stacks of Galois representations

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".

50 pages. 6 figures. Comments welcome