1 citations · 1 across the 5 of their papers we have counts for
5 papers
-cosheafification
Yuri Shimizu
Cosheaves are a dual notion of sheaves. In this paper, we prove existence of a dual of sheafifications, called \textit{cosheafifications}, in the -category theory. We also…
Universal birational invariants and -homology
Yuri Shimizu
Let be a field admitting a resolution of singularities. In this paper, we prove that the functor of zeroth -homology is universal as…
Relative -homology and its applications
Yuri Shimizu
In this paper, we prove an -homology version of the Whitehead theorem with dimension bound. We also prove an excision theorem for -homology, Suslin homo…
Notes on A^1-contractibility and A^1-excision
Yuri Shimizu
We prove that a smooth scheme of dimension over a perfect field is A^1-weakly equivalent to a point if it is A^1-n-connected. We also prove an excision result for A^1-homotopy…
The topological proof of the Poincare conjecture
Yuri Shimizu
We consider the operation to crush a subset of a manifold to one-point when the result of the crushing also be a manifold. Then the Poincare conjecture is split to two problems; fo…