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Descent in algebraic K-theory SemesterWiSe 2017 / 18 Lecturer Adeel Khan Type of course (Veranstaltungsart) Vorlesung Contents We will study the algebraic K-theory of derived schemes and stacks. Our focus will be on questions of descent, for which purpose we will revisit the celebrated paper of Thomason-Trobaugh [TT] and see how it can be extended to the world of derived algebraic geometry. More specifically, we will discuss two types of descent problems: first, descent for the Zariski and Nisnevich topologies; and secondly, descent by derived blow-ups (which has recently been established by Kerz-Strunk-Tamme [KST]). As far as time permits, we will also see some applications to the K-theory of classical schemes, including a pro-cdh-descent result and the resolution of Weibel's conjecture on negative K-theory (both also obtained in [KST]). Literature [TT] R.W. Thomason and T. Trobaugh, "Higher Algebraic K-Theory of Schemes and of Derived Categories" [L] Jacob Lurie, "Spectral Algebraic Geometry" [KST] Moritz Kerz, Florian Strunk, Georg Tamme, "Algebraic K-theory and descent for blow-ups" Recommended previous knowledge * Algebraic geometry (scheme theory, sites and sheaves) * Familiarity with the language of infinity-categories Time/Date Monday 14 - 16 Location SFB seminar room Course homepage http://www.preschema.com/teaching/ktheory-ws17/ (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MArGeo ECTS 3 |