Tate cohomology was originally defined over finite groups. More recently, Avramov and Martsinkovsky showed how to extend the definition so that it now works well over Gorenstein rings. This paper improves the theory further by giving a new definition that works over more general rings, specifically, those with a dualizing complex. The new definition of Tate cohomology retains the desirable prop...

We give a new proof of Kollár’s conjecture on the derived pushforward dualizing sheaf twisted by variation Hodge structure. This has been settled M. Saito via theory mixed modules and various applications in investigation Albanese maps. Our technique is $$L^2$$ theoretic which gives concrete constructions proofs to conjecture. The point view allows us generalize context non-abelian theory.

We study presentations of the virtual dualizing modules special linear groups number rings, Steinberg modules. Bykovskii gave a presentation for integers, and our main result is generalization this to Gaussian integers Eisenstein integers. also show that does not give several Euclidean rings.

This paper describes the historical background and motivation involved in the discovery (or invention) of Chu categories. In 1975, I began a sabbatical leave at the ETH in Zürich, with the idea of studying duality in categories in some depth. By this, I meant not such things as the duality between Boolean algebras and Stone spaces, nor between compact and discrete abelian groups, but rather sel...

We show that Liouville gravity arises as the limit of pure Einstein gravity in 2+ ε dimensions as ε goes to zero, provided Newton’s constant scales with ε. Our procedure – spherical reduction, dualization, limit, dualizing back – passes several consistency tests: geometric properties, interactions with matter and the Bekenstein-Hawking entropy are as expected from Einstein gravity. Platinum Jub...

A semi-dualizing module over a commutative noetherian ringA is a finitely generated module C with RHomA(C,C) ≃ A in the derived category D(A). We show how each such module gives rise to three new homological dimensions which we call C–Gorenstein projective, C–Gorenstein injective, and C–Gorenstein flat dimension, and investigate the properties of these dimensions.