Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Descent in algebraic K-theory
Semester
WiSe 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
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Passing the examination below
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 30 minutes, Date: individual appointment, re-exam: Date: individual
    appointment
Modules
BV, MV, MArGeo

ECTS
3