منابع مشابه
Zariski’s Main Theorem
By base change, i′n is also a closed embedding, hence affine. We have the unit map F → in∗i ′∗ n (F ). Applying Rf∗ gives a map Rf∗(F ) → Rf∗i ′ n∗i ′∗ n (F ). Since i ′ n is affine, Ri′n∗ ≃ i ′ n∗. By Leray’s spectral sequence, Rf∗i ′ n∗ ≃ R(f ◦ i ′ n)∗ ≃ R(in ◦ fn)∗ ≃ in∗Rfn∗. Applying H, we have a map Rf∗(F ) → R f∗i ′ n∗i ′∗ n (F ) ≃ in∗R fn∗(i ′∗ n (F )). Applying in∗i ∗ n to both sides an...
متن کاملAn optimal gap theorem
By solving the Cauchy problem for the Hodge-Laplace heat equation for d-closed, positive (1,1)-forms, we prove an optimal gap theorem for Kähler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius r centered at any fixed point o is a function of o(r−2). Furthermore via a relative monotonicity estima...
متن کاملPCP theorem: gap amplification
In this note, we prove the following theorem, which is a major step toward a proof of the PCP theorem. Recall that in the optimization problem 2-CSPW, we are given a list of arity-2 constraints between variables over an alphabet of size W and the goal is to find an assignment to the variables that satisfies as many of the constraints as possible. A 2-CSPW instance φ is d-regular if every variab...
متن کاملMain Theorem of Complex Multiplication
In [S, Ch. IV, §18] the Main Theorem of complex multiplication is proved in a manner that uses some adelic formalism. However, [S] uses a framework for algebraic geometry that has long been abandoned, so many of the beautiful ideas there are somewhat shrouded in mystery for the reader who is unfamiliar with the pre-Grothendieck approaches to algebraic geometry and abelian varieties. The aim of ...
متن کاملA Generalization of the Gap Forcing Theorem
The Main Theorem of this article asserts in part that if an extension V ⊆ V satisfies the δ approximation and covering properties, then every embedding j : V → N definable in V with critical point above δ is the lift of an embedding j ↾ V : V → N definable in the ground model V . It follows that in such extensions there can be no new weakly compact cardinals, totally indescribable cardinals, st...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Logic
سال: 2020
ISSN: 0219-0613,1793-6691
DOI: 10.1142/s0219061320500257