(1) Is the definition of [flop](http://en.wikipedia.org/wiki/Flip_%28algebraic_geometry%29) given by Wikipedia the industry standard?


(2) Regardless of the answer to (1), when is it expected that a birational transformation gives rise to a derived equivalence?


References to places where precise conjectures are recorded will be very much appreciated!


The reason I'm asking: apparently it is conjectured that different crepant resolutions are derived equivalent. On page 40 of [this](http://arxiv.org/abs/alg-geom/9506012) paper of Bondal-Orlov, they conjecture that flops induce derived equivalences. Apparently "flop" is sometimes used to mean birational transformation preserving canonical classes (without specifying the type of surgery actually being performed). So I'm interested to know whether such transformations are expected to be factorizable into (Wikipedia) flops, or produce derived equivalences for other reasons.



What is a flop (and when are they conjectured to give derived equivalences)?
I'm not any kind of expert on this stuff and I'm not sure what the current state of this conjecture is, but Kawamata has conjectures in [this paper](http://arxiv.org/PS_cache/math/pdf/0205/0205287v3.pdf) and [this paper](http://arxiv.org/PS_cache/math/pdf/0311/0311139v2.pdf) regarding when two birational varieties have equivalent derived categories. He also discusses flops in the first paper.


He has partial results, including: if $X$ is general type and $\mathcal{D}^b(X) \cong \mathcal{D}^b(Y)$ as triangulated categories then $X$ and $Y$ are K-equivalent. This generalizes the famous theorem of Bondal-Orlov that the bounded derived category of a Fano variety determines the variety. IIRC, in the proof of his theorem he takes the kernel of the Fourier-Mukai transform that gives the equivalence, shows that the support of the kernel (meaning the union of the supports of the cohomology sheaves of the kernel) has a component $Z$ dominating both varieties and uses $Z$ for the "roof" of the K-equivalence. The assumption that $X$ is general type is used to show that the projections from $Z$ are birational.


