Skip to main content
MathOverflow

Return to Question

edited tags
Link
Mikhail Bondarko
Mikhail Bondarko
  • 16.9k
  • 4
  • 34
  • 97
added 13 characters in body
Source Link
Francesco Polizzi
Francesco Polizzi
  • 66.3k
  • 5
  • 180
  • 283

Let $X$ and $Y$ be two nonsingular projective varieties defined over the complex numbers. If $X$ and $Y$ are $\mathbb{A}^1$-homotopy equivalent, then does $X$ satisfying the Hodge conjecture imply that $Y$ satisfies the Hodge conjecture?

If $X$ and $Y$ are $\mathbb{A}^1$-homotopy equivalent, then does $X$ satisfying the Hodge conjecture imply that $Y$ satisfies the Hodge conjecture?

Let $X$ and $Y$ be two nonsingular projective varieties over the complex numbers. If $X$ and $Y$ are $\mathbb{A}^1$-homotopy equivalent, then does $X$ satisfying the Hodge conjecture imply that $Y$ satisfies the Hodge conjecture?

Let $X$ and $Y$ be two nonsingular projective varieties defined over the complex numbers.

If $X$ and $Y$ are $\mathbb{A}^1$-homotopy equivalent, then does $X$ satisfying the Hodge conjecture imply that $Y$ satisfies the Hodge conjecture?

Source Link
user94803
user94803

Is the Hodge Conjecture an $\mathbb{A}^1$-homotopy invariant?

Let $X$ and $Y$ be two nonsingular projective varieties over the complex numbers. If $X$ and $Y$ are $\mathbb{A}^1$-homotopy equivalent, then does $X$ satisfying the Hodge conjecture imply that $Y$ satisfies the Hodge conjecture?