منابع مشابه
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We carefully develop the theory of Serre duality and dualizing sheaves. We differ from the approach in [12] in that the use of spectral sequences and the Yoneda pairing are emphasized to put the proofs in a more systematic framework. As applications of the theory, we discuss the RiemannRoch theorem for curves and Bott’s theorem in representation theory (following [8]) using the algebraic-geomet...
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Suppose X is a smooth projective scheme of finite type over a field K, E is a locally free OX -bimodule of rank 2, A is the non-commutative symmetric algebra generated by E and ProjA is the corresponding non-commutative P -bundle. We use the properties of the internal Hom functor HomGrA(−,−) to prove versions of Serre finiteness and Serre vanishing for ProjA. As a corollary to Serre finiteness,...
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We prove Serre’s conjecture for the case of Galois representations with Serre’s weight 2 and level 1. We do this by combining the potential modularity results of Taylor and lowering the level for Hilbert modular forms with a Galois descent argument, properties of universal deformation rings, and the non-existence of p-adic Barsotti-Tate conductor 1 Galois representations proved in [Di3].
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2018
ISSN: 1435-9855
DOI: 10.4171/jems/826