منابع مشابه
Integral Grothendieck-riemann-roch Theorem
in the Chow ring with rational coefficients CH(S)Q = ⊕nCH (S)Q. Here ch is the Chern character and Td(TX), Td(TS) stand for the Todd power series evaluated at the Chern classes of the tangent bundle of X, respectively S. Since both sides of (1.1) take values in CH(S)Q := CH (S)⊗Q, only information modulo torsion about the Chern classes of f∗[F ] can be obtained from this identity. The goal of o...
متن کاملThe Grothendieck-riemann-roch Theorem for Varieties
We give an exposition of the Grothendieck-Riemann-Roch theorem for algebraic varieties. Our proof follows Borel and Serre [3] and Fulton [5] closely, emphasizing geometric considerations and intuition whenever possible.
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Grothendieck proved that if f : X −→ Y is a proper morphism ofnice schemes, then Rf∗ has a right adjoint, which is given as tensor productwith the relative canonical bundle. The original proof was by patching localdata. Deligne proved the existence of the adjoint by a global argument, andVerdier showed that this global adjoint may be computed locally.In this article we show ...
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We prove that for a normal projective variety X in characteristic 0, and a base-point free ample line bundle L on it, the restriction map of divisor class groups Cl(X) → Cl(Y ) is an isomorphism for a general member Y ∈ |L| provided that dimX ≥ 4. This is a generalization of the Grothendieck-Lefschetz theorem, for divisor class groups of singular varieties. We work over k, an algebraically clos...
متن کاملPdmi Preprint | 25/1998 on a Theorem of Grothendieck
It is considered a smooth projective morphism p : T ! S to a smooth variety S. It is proved, in particular, the following result. The total direct image Rp (Z=nZ) of the constant etale sheaf Z=nZis locally for Zarisky topology quasi-isomorphic to a bounded complex L on S consisting of locally constant constructible etale Z=nZ-module sheaves.
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2018
ISSN: 0024-6115,1460-244X
DOI: 10.1112/plms.12200