The projective line associated with a strongly Z-graded ring

07/12/2018, 14:00 - 15:00 in MAP/0G/017

Montgomery, Tasha (Queen’s University Belfast)


Abstract:

It is known that the algebraic K– theory of the projective line over an arbitrary commutative ring splits into two copies of the K-theory of the ground ring. This was generalised, by Bass (’68) and Quillen (’73), to non-commutative rings. My aim for this talk is to give a further generalisation, by introducing a projective line associated to a Z-graded ring.
The process, perhaps surprisingly, works much like in the “classical” case, however new phenomena are quickly encountered. For example, the familiar family of twisting sheaves from algebraic geometry now depends on a two-parameter construction as opposed to just one. After presenting the outline of the proof, in the case of the projective line, I hope to give some details regarding my ongoing work on the projective plane.
This is part of my ongoing PhD thesis project under the supervision of Dr Thomas Hüttemann.