talk by E. Aldrovandi

[Ugo Bruzzo]

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SISSA GEOMETRY SEMINAR
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Professor Ettore Aldrovandi (Florida State University,
Tallahassee) will give a talk on

Stacks and non-abelian cohomology

on Tuesday, June 29 at 4:00 pm, Room 136

Abstract:

Morphisms of gr-stacks (stacks with a group law) can be encoded
by certain diagrams of group objects called butterflies.  They
compute the derived mapping space between two complexes (of
length 2) of non-necessarily abelian group.  In the abelian case,
this is Deligne's old result characterizing the derived category
in terms of morphisms of Picard stacks.

After describing the general theory, we describe two applications
to non-abelian cohomology: (1) the long exact sequence arising
from a given appropriately defined short exact sequence of
gr-stacks; and (2) the change of coefficient map arising from a
given morphism of gr-stacks.  We will point out how these
constructions differ from (and reduce to) the standard ones in
homological algebra.

Time permitting, I will sketch how these ideas generalize to
higher stacks.

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U. Bruzzo


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