3 problems

Moduli conjecture for A^1-contractible smooth varieties
Moduli conjecture. For every $m\geq 3$ and every $n\geq 0$ , there exists such an $S$ and $f$ for which the fibers over the $k$ -points of $S$ are all non-isomorphic.
opena1-homotopy affine-varieties moduli
0 responses
04
The ^1-connectedness conjecture for reductive algebraic groups
The conjecture. For every field extension $F$ of $k$ ,
opena1-homotopy algebraic-groups r-equivalence
0 responses
03
Morel's conjecture on rational points in the -homotopy category
Let $F$ be the base field, let $X$ be a smooth variety over $F$ , and write … to $X$ in this category. Define an equivalence relation on $X(F)$ generated by elementary $^1$ -homotopi…
opena1-homotopy algebraic-geometry birational-geometry
0 responses
04

Moduli conjecture for A^1-contractible smooth varieties