Companion forms and Kodaira-Spencer theory

DOI10.1007/BF01231333zbMath0770.11024OpenAlexW2064846883WikidataQ56813948 ScholiaQ56813948MaRDI QIDQ1209134

Robert F. Coleman, José Felipe Voloch

Publication date: 16 May 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144051

zbMATH Keywords

Galois representation\(p\)-divisible groupcompanion formmodular elliptic curvestame ramificationcuspidal eigenformde Rham cohomology of the Igusa curveKodaira-Spencer pairingSerre-Tate pairingTate module of the Jacobian

Mathematics Subject Classification ID

Elliptic curves (14H52) Holomorphic modular forms of integral weight (11F11) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) (p)-adic cohomology, crystalline cohomology (14F30) Formal groups, (p)-divisible groups (14L05)

Related Items (16)

Crystalline cohomology and \(GL(2,\mathbb{Q})\) ⋮ Companion forms over totally real fields. II ⋮ On Serre's conjecture for mod \(\ell \) Galois representations over totally real fields ⋮ A Serre weight conjecture for geometric Hilbert modular forms in characteristic \(p\) ⋮ Companion forms for unitary and symplectic groups ⋮ Modularity lifting beyond the Taylor-Wiles method ⋮ On automorphy of certain Galois representations of \(\mathrm{GO}_{4}\)-type ⋮ PGL2(𝔽ℓ) number fields with rational companion forms ⋮ Hecke stability and weight 1 modular forms ⋮ Companion forms over totally real fields ⋮ THE WEIGHT PART OF SERRE’S CONJECTURE FOR ⋮ On modular mod \(\ell\) Galois representations with exceptional images ⋮ The weight in Serre's conjectures on modular forms ⋮ UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ATTACHED TO HILBERT MODULAR FORMS MOD  OF WEIGHT 1 ⋮ Serre's modularity conjecture. I ⋮ Serre's modularity conjecture. II

Cites Work

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• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• Algebraic solutions of differential equations (p-curvature and the Hodge filtration)
• The weight in Serre's conjectures on modular forms
• A tameness criterion for Galois representations associated to modular forms (mod \(p\))
• The generic Torelli theorem for the Prym map
• Theta functions on Riemann surfaces
• Logarithmic structures of Fontaine-Illusie. II
• Formes modulaires de poids $1$
• Les Schémas de Modules de Courbes Elliptiques

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