Geodesic
Iwasawa–Greenberg main conjecture for nonordinary modular forms and Eisenstein congruences on GU(3,1)
Forum of Mathematics, Sigma, Tome 10 (2022)

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In this paper, we prove one divisibility of the Iwasawa–Greenberg main conjecture for the Rankin–Selberg product of a weight two cusp form and an ordinary complex multiplication form of higher weight, using congruences between Klingen Eisenstein series and cusp forms on $\mathrm {GU}(3,1)$, generalizing an earlier result of the third-named author to allow nonordinary cusp forms. The main result is a key input in the third-named author’s proof of Kobayashi’s $\pm $-main conjecture for supersingular elliptic curves. The new ingredient here is developing a semiordinary Hida theory along an appropriate smaller weight space and a study of the semiordinary Eisenstein family. 
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     author = {Francesc Castella and Zheng Liu and Xin Wan},
     title = {Iwasawa{\textendash}Greenberg main conjecture for nonordinary modular forms and {Eisenstein} congruences on {GU(3,1)}},
     journal = {Forum of Mathematics, Sigma},
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Francesc Castella; Zheng Liu; Xin Wan. Iwasawa–Greenberg main conjecture for nonordinary modular forms and Eisenstein congruences on GU(3,1). Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.95

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