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Weight structures for triangulated categories; some motivic examples

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Mikhail Bondarko
St. Petersburg State U./MPI
Don, 01/07/2010 - 15:00 - 16:00
MPIM Lecture Hall
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My talk is dedicated to weight structures. Weight structures are natural counterparts of  $t$-structures (for triangulated categories); the simplest examples of weight structures come from stupid truncations of complexes (whereas $t$-structures are related with canonical truncations). Weight structures yield (functorial) weight complexes,  weight filtrations, and  weight spectral sequences.  An example: a conservative exact weight complex functor from the Voevodsky's category of geometric motives to $K^b(Chow)$. Partial cases of weight spectral sequences are:  Deligne's weight spectral sequences (for singular and 'etale cohomology), coniveau spectral sequences, and Atiyah-Hirzebruch spectral sequences; the weight structure method yields strong functoriality results for these spectral sequences and for the corresponding ('weight') filtrations. All of these examples will be mentioned in the talk (though the time is not sufficient to describe them in detail). I will also mention the relation of weight structures with $t$-structures, certain 'functoriality' of weight structures, and the relation of weight structures with the calculation of certain $K_0$-groups.

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