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Fibrés d'intersection
Let f : X → S be a projective morphism of Noetherian schemes. We assume f purely of relative dimension d and finite Tor-dimensional. We associate to d +1...
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Rigid Curves in Complete Intersection Calabi–Yau Threefolds
Working over the complex numbers, we study curves lying in a complete intersection K3 surface contained in a (nodal) complete intersection Calabi–Yau...
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Weight-Monodromy Conjecture for ℓ-Adic Representations Associated to Modular Forms
The purpose of this short paper is to state the weight-monodromy conjecture for ℓ-adic representation associated to modular forms, which is...
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Finiteness of Torsion in the Codimension-Two Chow Group: An Axiomatic Approach
The author gives an overview on recent progress in the study of torsion zero cycles. The new methods that have been developped to obtain finiteness...
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Algebraic Cycles on Abelian Varieties
We give a survey of the Fourier-Mukai transform on abelian varieties. This is a correspondence from an abelian variety to its dual abelian variety,...
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Algebraic Cycle Complexes
We collect several basic properties of algebraic cycle complexes defined by Bloch, Friedlander, Suslin and Voevodsky, like moving lemmas,...
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Lectures on Algebro-Geometric Chern-Weil and Cheeger-Chern-Simons Theory for Vector Bundles
An algebraic theory of differential characters [16], [17] is outlined. A Riemann-Roch theorem for regular flat bundles, using a weak form of these...
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Motives and Filtrations on Chow Groups, II
In this paper sequential to [Sa], we discuss a philosophy of Bloch and Beilinson concerning filtrations on Chow groups of algebraic vareties, which...
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Cohomology Computations Related to the ι-Adic Abel-Jacobi Map Modulo ι
Let k be a field, \( \bar k \) a separable closure and...
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The K-theory of fields in characteristic p
We show that for a field k of characteristic p, H i (k ,ℤ( n )) is uniquely p -divisible for i ≠ n (we use higher Chow groups as our definition of motivic...
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Equivalence Relations on Algebraic Cycles
Algebraic cycles give rise to important invariants of algebraic varieties, and it is common to study the groups of algebraic cycles via so-called...
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Zero Cycles on Singular Varieties
In this article, we survey some of the known results on the Chow group of 0-cycles on singular varieties, including some fairly recent results. Along...
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On the commutativity of localized Chern characters with refined Gysin homomorphisms
We give a simple proof of the fact that the localized Chern characters of Baum, Fulton and MacPherson commute with the refined Gysin homomorphisms...
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Lefschetz Motives and the Tate Conjecture
A Lefschetz class on a smooth projective variety is an element of the Q-algebra generated by divisor classes. We show that it is possible to define...
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The generalized Hodge conjecture for the quadratic complex of lines in projective four–space
We verify the generalized Hodge conjecture GHC(X,5,2) for the quadratic complex of lines in projective four–space.
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Motives of Uniruled 3-Folds
J. Murre has conjectured that every smooth projective variety X of dimension d admits a decomposition of the diagonal δ=p 0 +...+p 2d ∈ CH d (X × X) ⊗ Q...