Hurewicz Fibrations Need Not be Locally Trivial

Numerically Trivial Fibrations

We develop an intersection theory for a singular hermitian line bundle with positive curvature current on a smooth projective variety and irreducible curves on the variety. And we prove the existence of a natural rational fibration structure associated with the singular hermitian line bundle. Also for any pseudoeffective line bundle on a smooth projective variety, we prove the existence of a na...

Locally Trivial Torsors That Are Not Weil-châtelet Divisible

For every prime p we give infinitely many examples of torsors under abelian varieties over Q that are locally trivial but not divisible by p in the Weil-Châtelet group. We also give an example of a locally trivial torsor under an elliptic curve over Q which is not divisible by 4 in the Weil-Châtelet group. This gives a negative answer to a question of Cassels.

Locally trivial W∗-bundles

Monads Need Not Be Endofunctors

We introduce a generalisation of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed λ-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions...

Selfishness need not be bad

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