nLab B1-homotopy theory

Idea

$\mathbb{B}^1$-homotopy theory is the study of the localization of an (∞,1)-sheaf (∞,1)-category over a site of analytic spaces at morphisms $\mathbb{B}^1 \to *$, where $\mathbb{B}^1 \simeq Spm(k\{t\})$ is the Tate ball.

Related concepts

• A1-homotopy theory

• complex analytic ∞-groupoid

References

• Joseph Ayoub, Motives of rigid varieties and

  the motivic nearby functor_, talk notes 2006 (pdf)

• Joseph Ayoub, Motifs des variétés analytiques rigides (pdf)

• Joseph Ayoub, Floian Ivorra and Julien Sebag, Motives of rigid analytic tubes and nearby motivic sheaves (pdf)