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- Standard_conjectures_on_algebraic_cycles abstract "In mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories. One of the original applications of these conjectures, envisaged by Alexander Grothendieck, was to prove that his construction of pure motives gave an abelian category that is semisimple. Moreover, as he pointed out, the standard conjectures also imply the hardest part of the Weil conjectures, namely the "Riemann hypothesis" conjecture that remained open at the end of the 1960s and was proved later by Pierre Deligne; for details on the link between Weil and standard conjectures, see Kleiman (1968). The standard conjectures remain open problems, so that their application gives only conditional proofs of results. In quite a few cases, including that of the Weil conjectures, other methods have been found to prove such results unconditionally.The classical formulations of the standard conjectures involve a fixed Weil cohomology theory H. All of the conjectures deal with "algebraic" cohomology classes, which means a morphism on the cohomology of a smooth projective varietyH ∗(X) → H ∗(X) induced by an algebraic cycle with rational coefficients on the product X × X via the cycle class map, which is part of the structure of a Weil cohomology theory.".
- Standard_conjectures_on_algebraic_cycles wikiPageExternalLink StandardConjs.pdf.
- Standard_conjectures_on_algebraic_cycles wikiPageID "10470079".
- Standard_conjectures_on_algebraic_cycles wikiPageRevisionID "605395911".
- Standard_conjectures_on_algebraic_cycles hasPhotoCollection Standard_conjectures_on_algebraic_cycles.
- Standard_conjectures_on_algebraic_cycles subject Category:Algebraic_geometry.
- Standard_conjectures_on_algebraic_cycles subject Category:Conjectures.
- Standard_conjectures_on_algebraic_cycles type Abstraction100002137.
- Standard_conjectures_on_algebraic_cycles type Cognition100023271.
- Standard_conjectures_on_algebraic_cycles type Concept105835747.
- Standard_conjectures_on_algebraic_cycles type Conjectures.
- Standard_conjectures_on_algebraic_cycles type Content105809192.
- Standard_conjectures_on_algebraic_cycles type Hypothesis105888929.
- Standard_conjectures_on_algebraic_cycles type Idea105833840.
- Standard_conjectures_on_algebraic_cycles type PsychologicalFeature100023100.
- Standard_conjectures_on_algebraic_cycles type Speculation105891783.
- Standard_conjectures_on_algebraic_cycles comment "In mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories. One of the original applications of these conjectures, envisaged by Alexander Grothendieck, was to prove that his construction of pure motives gave an abelian category that is semisimple.".
- Standard_conjectures_on_algebraic_cycles label "Standard conjectures on algebraic cycles".
- Standard_conjectures_on_algebraic_cycles label "代数的サイクルの標準予想".
- Standard_conjectures_on_algebraic_cycles sameAs 代数的サイクルの標準予想.
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- Standard_conjectures_on_algebraic_cycles sameAs Q7598336.
- Standard_conjectures_on_algebraic_cycles sameAs Q7598336.
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- Standard_conjectures_on_algebraic_cycles wasDerivedFrom Standard_conjectures_on_algebraic_cycles?oldid=605395911.
- Standard_conjectures_on_algebraic_cycles isPrimaryTopicOf Standard_conjectures_on_algebraic_cycles.