August 12, 2025Open Access

Hodge and generalized Hodge conjectures, coniveau and algebraic cycles

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The hodge conjecture proposes a relationship between algebraic cycles and topological properties.
Emphasizing the generalized hodge conjecture, which broadens the scope of hodge structures and algebraic cycles.
This survey builds on existing theories in algebraic geometry, focusing on connections and implications within the field.
Insights from this work may enhance the understanding of algebraic cycles and their significance in various mathematical contexts.

Implication

This survey highlights the hodge conjecture and its relation to generalized hodge conjecture in algebraic cycles and motives.

Abstract

This is a survey of the Hodge conjecture, with emphasis on its companion, the generalized Hodge conjecture, which involves the theory of Hodge structures, algebraic cycles and motives.

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Cite This Study

Claire Voisin (2025) studied this question.

synapsesocial.com/papers/68af494dad7bf08b1ead4c58 https://doi.org/10.56994/jomp.001.001.002

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Implication

This survey highlights the hodge conjecture and its relation to generalized hodge conjecture in algebraic cycles and motives.

Abstract

This is a survey of the Hodge conjecture, with emphasis on its companion, the generalized Hodge conjecture, which involves the theory of Hodge structures, algebraic cycles and motives.

Hodge and generalized Hodge conjectures, coniveau and algebraic cycles

Key Points

Implication

Abstract

Discussion

Cite This Study

Hodge and generalized Hodge conjectures, coniveau and algebraic cycles

Key Points

Implication

Abstract

Discussion

Cite This Study

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