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A Categorical Formulation Of Algebraic Geometry, Bradley Willocks
A Categorical Formulation Of Algebraic Geometry, Bradley Willocks
Doctoral Dissertations
We construct a category, $\Omega$, of which the objects are pointed categories and the arrows are pointed correspondences. The notion of a ``spec datum" is introduced, as a certain relation between categories, of which one has been given a Grothendieck topology. A ``geometry" is interpreted as a sub-category of $\Omega$, and a formalism is given by which such a subcategory is to be associated to a spec datum, reflecting the standard construction of the category of schemes from the category of rings by affine charts.
Equations For Nilpotent Varieties And Their Intersections With Slodowy Slices, Benjamin Johnson
Equations For Nilpotent Varieties And Their Intersections With Slodowy Slices, Benjamin Johnson
Doctoral Dissertations
This thesis investigates minimal generating sets of ideals defining certain nilpotent varieties in simple complex Lie algebras. A minimal generating set of invariants for the whole nilpotent cone is known due to Kostant. Broer determined a minimal generating set for the subregular nilpotent variety in all simple Lie algebra types. I extend Broer's results to two families of nilpotent varieties, valid in any simple Lie algebra, that include the nilpotent cone, the subregular case, and usually more. In the first part of my thesis I describe a minimal generating set for the ideal of each of these varieties in the …