

Shafarevich Seminar
March 3, 2020 15:00, Moscow, online






Highest weight approximations of chain abelian categories
A. Bodzenta^{} 
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Abstract:
I will describe the construction
of highest weight categories as abelian envelopes of thin exact
categories, i.e. exact categories with 'full exceptional
collections'. I will discuss a source of examples of thin exact
categories given by slender filtrations on abelian categories, i.e.
filtrations with graded factors equivalent to the category of vector
spaces. In geometry, slender filtrations appear naturally for
sandwiched surface singularities. For cyclic quotient singularities,
or their algebraic counterpart  chain abelian categories, I will
classify all possible slender filtrations and calculate the abelian
envelopes of the thin exact categories they give. I will show that
they are all derived equivalent. This is a joint work in progress
with A. Bondal.
Language: English

