Results 301 to 310 of about 163,993 (328)
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2007
Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity.
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Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity.
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Intersection of algebraic cycles
Journal of Mathematical Sciences, 1996In this expository paper, the author explains with illustrating examples why intersection homology is needed to recover some properties of intersection of cycles and of Poincaré duality both of which fail when one uses the classical homology theory for singular pseudomanifolds.
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ON ALGEBRAIC CYCLES ON ABELIAN VARIETIES
Mathematics of the USSR-Izvestiya, 1978Let be a simple 4-dimensional abelian variety of the first or second type in Albert's classification (i.e. all simple factors of the -algebra are isomorphic to or ). In this case the algebra over is generated by divisor classes. If , and the Hodge group has type or , then and the -space is not generated by classes of intersections of divisors ...
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1984
If T is a non-singular curve, and p: S → is a morphism, any (k+ 1)-cycle \( \alpha = \sum {n_i}\left[ {{\mathfrak{F}_i}} \right] \) On S determines an algebraic family of k-cycles αt, on the fibres Y t =P -1 (t): $$ {\alpha _t} = \begin{array}{*{20}{c}} \sum \\ {{\gamma _i}} \end{array}{n_i}\left[ {{{\left( {{V_i}} \right)}_t}} \right] $$
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If T is a non-singular curve, and p: S → is a morphism, any (k+ 1)-cycle \( \alpha = \sum {n_i}\left[ {{\mathfrak{F}_i}} \right] \) On S determines an algebraic family of k-cycles αt, on the fibres Y t =P -1 (t): $$ {\alpha _t} = \begin{array}{*{20}{c}} \sum \\ {{\gamma _i}} \end{array}{n_i}\left[ {{{\left( {{V_i}} \right)}_t}} \right] $$
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2010
Spencer Bloch's 1979 Duke lectures, a milestone in modern mathematics, have been out of print almost since their first publication in 1980, yet they have remained influential and are still the best place to learn the guiding philosophy of algebraic cycles and motives.
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Spencer Bloch's 1979 Duke lectures, a milestone in modern mathematics, have been out of print almost since their first publication in 1980, yet they have remained influential and are still the best place to learn the guiding philosophy of algebraic cycles and motives.
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The marine nitrogen cycle: new developments and global change
Nature Reviews Microbiology, 2022David A Hutchins, Douglas G Capone
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Human and environmental safety of carbon nanotubes across their life cycle
Nature Reviews Materials, 2023Dana Goerzen, Matteo Pasquali
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Balancing interfacial reactions to achieve long cycle life in high-energy lithium metal batteries
Nature Energy, 2021Chaojiang Niu, Joshua A Lochala, Xia Cao
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