Some computations of algebraic cycle homology

K-Theory ◽  
1994 ◽  
Vol 8 (3) ◽  
pp. 271-285 ◽  
Author(s):  
Eric M. Friedlander
Keyword(s):  
Algebraic Cycle

scholarly journals Deformation of algebraic cycle classes in characteristic zero

2014 ◽  
Vol 1 (3) ◽  
pp. 290-310 ◽  
Author(s):  
Spencer Bloch ◽  
Hélène Esnault ◽  
Moritz Kerz
Keyword(s):  
Characteristic Zero ◽  
Algebraic Cycle ◽  
Cycle Classes

scholarly journals p-adic deformation of algebraic cycle classes

2013 ◽  
Vol 195 (3) ◽  
pp. 673-722 ◽  
Author(s):  
Spencer Bloch ◽  
Hélène Esnault ◽  
Moritz Kerz
Keyword(s):  
Algebraic Cycle ◽  
Cycle Classes

The Spread Philosophy in the Study of Algebraic Cycles

2017 ◽  
Author(s):  
Mark L. Green
Keyword(s):  
Hodge Structure ◽  
Hodge Theory ◽  
Algebraic Cycles ◽  
Algebraic Cycle ◽  
Integral Lattice ◽  
Group Of Automorphisms ◽  
Intersection Pairing ◽  
Variation Of Hodge Structure

This chapter discusses the spread philosophy in the study of algebraic cycles, in order to make use of a geometry by considering a variation of Hodge structure where D is the Hodge domain (or the appropriate Mumford–Tate domain) and Γ‎ is the group of automorphisms of the integral lattice preserving the intersection pairing. If we have an algebraic cycle Z on X, taking spreads yields a cycle Ƶ on X. Applying Hodge theory to Ƶ on X gives invariants of the cycle. Another related situation is algebraic K-theory. For example, to study Kₚsuperscript Milnor(k), the geometry of S can be used to construct invariants.

scholarly journals A Dual of the Chow Transformation

2018 ◽  
Vol 5 (1) ◽  
pp. 158-194
Author(s):  
Michel Méo
Keyword(s):  
Projective Space ◽  
Integral Geometry ◽  
Inversion Formula ◽  
Complex Projective Space ◽  
General Scheme ◽  
Algebraic Cycle ◽  
Left Inverse ◽  
Positive Current ◽  
Closed Positive Current ◽  
Complex Projective

AbstractWe define a dual of the Chow transformation of currents on the complex projective space. This transformation factorizes a left inverse of the Chow transformation and its composition with the Chow transformation is a right inverse of a linear diferential operator. In such a way we complete the general scheme of integral geometry for the Chow transformation. On another hand we prove the existence of a well defined closed positive conormal current associated to every closed positive current on the projective space. This is a consequence of the existence of a dual current, defined on the dual projective space. This allows us to extend to the case of a closed positive current the known inversion formula for the conormal of the Chow divisor of an effective algebraic cycle.

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