RAMIFIED DEFORMATION PROBLEMS BRIAN CONRAD Introduction The proof of the semistable Taniyama-Shimura Conjecture by Wiles [22] and Taylor-Wiles [21] uses as its central tool the deformation theory of Galois representation

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• Algebraic number theory
• Galois theory
• Frobenius endomorphism
• Galois module
• Group scheme
• Dieudonné module
• Étale morphism
• Finite field
• Abstract algebra
• Algebra
• Algebraic groups