The Eilenberg–Watts theorem over schemes

The Eilenberg-watts Theorem over Schemes

We describe obstructions to a direct limit preserving right exact functor between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. When the domain scheme is affine, all obstructions vanish and we recover the Eilenberg-Watts Theorem. We use our description of these obstructions to prove that if a direct limit preserving right exact functor F from a s...

2 00 9 the Eilenberg - Watts Theorem over Schemes

We study obstructions to a direct limit preserving right exact functor F between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. When the domain scheme is affine, or if F is exact, all obstructions vanish and we recover the Eilenberg-Watts Theorem. This result is crucial to the proof that the noncommutative Hirzebruch surfaces constructed in [3] ar...

An Assmus-Mattson theorem for codes over commutative association schemes

2 7 Fe b 20 09 THE EILENBERG - WATTS THEOREM OVER SCHEMES

We describe obstructions to a direct limit preserving right exact functor between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. When the domain scheme is affine, all obstructions vanish and we recover the Eilenberg-Watts Theorem. We use our description of these obstructions to prove that if a direct limit preserving right exact functor F from a s...

Mnëv’s Universality Theorem for Schemes

We prove a scheme-theoretic version of Mnëv’s Universality Theorem, suitable to be used in the proof of Murphy’s Law in Algebraic Geometry [Va, Main Thm. 1.1]. Somewhat more precisely, we show that any singularity type of finite type over Z appears on some incidence scheme of points and lines, subject to some particular further constraints. This paper is dedicated to Joe Harris on the occasion ...