인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.

Arithmetic duality theorems

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Infinite Abelian Groups

Cohen‐macaulay modules over cohen‐macaulay rings

Using a codimension-$1$ algebraic cycle obtained from the Poincare line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety $A$ and showed that the Fourier transform induces a decomposition of the Chow ring $CH^*(A)$. By using a codimension-$2$ algebraic cycle representing the Beauville--Bogomolov class, we give evidence for the existence of a similar decomposition for the Chow ring of hyperKahler varieties deformation equivalent to the Hilbert scheme of length-$2$ subschemes on a K3 surface. We indeed establish the existence of such a decomposition for the Hilbert scheme of length-$2$ subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

The Fourier transform for certain hyperKaehler fourfolds

Let f : X → B be a projective surjective morphism between quasi-projective varieties. The goal of this paper is the study of the Chow groups of X in terms of the Chow groups of B and of the fibres of f. One of the applications concerns quadric bundles. When X and B are smooth projective and when f is a flat quadric fibration, we show that the Chow motive of X is "built" from the motives of varieties of dimension less than the dimension of B.

Algebraic Cycles and Fibrations

Using a codimension-1 algebraic cycle obtained from the Poincare line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle representing the Beauville-Bogomolov class, we give evidence for the existence of a similar decomposition for the Chow ring of hyperKahler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. We indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

The Fourier Transform for Certain Hyperkahler Fourfolds

Let X be a complex smooth projective variety of dimension d Under some assump- tion on the cohomology of X, we construct mutually orthogonal idempotents in CHd(X X) Q whose action on algebraically trivial cycles coincides with the Abel{Jacobi map Such a con- struction generalizes Murre's construction of the Albanese and Picard idempotents and makes it possible to give new examples of varieties admitting a self-dual Chow{Kunneth decomposi- tion as well as new examples of varieties having a Kimura nite dimensional Chow motive For instance, we prove that fourfolds with Chow group of zero-cycles supported on a curve (eg rationally connected fourfolds) have a self-dual Chow{Kunneth decomposition We also prove that hypersurfaces of very low degree are Kimura nite dimensional

Projectors on the intermediate algebraic jacobians

A motive over a field $k$ is of abelian type if it belongs to the thick and rigid subcategory of Chow motives spanned by the motives of abelian varieties over $k$. This paper contains three sections of independent interest. First, we show that a motive which becomes of abelian type after a base field extension of algebraically closed fields is of abelian type. Given a field extension $K/k$ and a motive $M$ over $k$, we also show that $M$ is finite-dimensional if and only if $M_K$ is finite-dimensional. As a corollary, we obtain Chow--Kuenneth decompositions for varieties that become isomorphic to an abelian variety after some field extension. Second, let $\Omega$ be a universal domain containing $k$. We show that Murre's conjectures for motives of abelian type over $k$ reduce to Murre's conjecture (D) for products of curves over $\Omega$. In particular, we show that Murre's conjecture (D) for products of curves over $\Omega$ implies Beauville's vanishing conjecture on abelian varieties over $k$. Finally, we give criteria on Chow groups for a motive to be of abelian type. For instance, we show that $M$ is of abelian type if and only if the total Chow group of algebraically trivial cycles $CH_*(M_\Omega)_{alg}$ is spanned, via the action of correspondences, by the Chow groups of products of curves. We also show that a morphism of motives $f: N \to M$, with $N$ Kimura finite-dimensional, which induces a surjection $f_* : CH_*(N_\Omega)_{alg} \to CH_*(M_\Omega)_{alg}$ also induces a surjection $f_* : CH_*(N_\Omega)_{hom} \to CH_*(M_\Omega)_{hom}$ on homologically trivial cycles.

Charles Vial

Papers

The Fourier transform for certain hyperKaehler fourfolds

Algebraic Cycles and Fibrations

The Fourier Transform for Certain Hyperkahler Fourfolds

Projectors on the intermediate algebraic jacobians

Remarks on motives of abelian type