Hodge and generalized Hodge conjectures, coniveau and algebraic cycles | Synapse
August 12, 2025Open Access
Hodge and generalized Hodge conjectures, coniveau and algebraic cycles
Key Points
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.
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.