^Using linear algebra and algebraic geometry over a sufficiently large field, Joel Friedman proved that ∑g ∈ Gr(X∩gY) <= r(X)r(Y). He showed that this inequality implies the strengthened Hanna Neumann conjecture. We simplify Friedman's proof of the foregoing inequality by replac…
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form …
This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. This has theoretical advantages such as greater perspe…
"This work applies Gabber's theorem on alterations to Veovodsky's work on mixed motives ... Two applications are an isomorphism to Suslin that compares higher Chow groups and étale cohomology, and calculation of the motivic Steenrod algebra"--Back cover.
"The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples…