February 9, 2010

Plan

Posted in algebraic geometry at 8:49 am by noncommutativeag

I plan to write something on three topics:

1. Several basic spectrum for noncommutative ring and how do them come into the story of representation theory of reductive Lie algebra.

I will do some explicit computations. The motivation for me is for the research topic course which is now given by A.Rosenberg.I want to understand all of them in detail.

2. I will start with Zariski topology in commutative algebraic geometry and try to do direct imitation for noncommutative ring.

Unfortunately, one will find direct imitation failed. Therefore, another appropriate topology for noncommutative algebraic geometry will be formulated.After finish it, I will go to the purely functorial point of view to algebraic geometry. I might restrict myself to commutative algebraic geometry.

3. D-module theory and Lie algebra and their quantum analogue

I will talk about how noncommutative algebraic geometry naturally comes into the life of D-modules. I will push myself to write localization theory for category of D-modules in almost full details.

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2 Comments »

  1. Bryan said,

    Number 2 sounds particularly good(of course the others will be interesting), I can’t wait!


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