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= Introduction = <ref name="Blo81"/> <ref name="Goe07"/> <ref name="Gon95"/> <ref name="Lew81"/> <ref name="Sus84"/> <ref name="Zic15"/> <ref name="Sus91"/> <ref name="Sus87"/> <ref name="Blo91"/> Not: <ref name="Hut13"/> but has an informative introduction... = Schedule = {| border="1" style="text-align:left;" | 20.4. |[[#Introduction|Introduction]] |Braeunling |- | 27.4. |[[#Cech cohomology and the Hodge conjecture in codim 1|Cech cohomology and the Hodge conjecture in codim 1]] |N.N. |- | 4.5. |[[#Chow groups and Chern classes|Chow groups and Chern classes]] |N.N. |- | 11.5. |[[#Elementary algebraic K-Theory: K0 and K1|Elementary algebraic K-Theory: K0 and K1]] |N.N. |- | 18.5. |Pentecost | |- | 25.5. |[[#Elementary algebraic K-Theory: K2|Elementary algebraic K-Theory: K2]] |N.N. |- | 1.6. |[[#Cycles in Codimension 2, part I|Cycles in Codimension 2, part I]] |N.N. |- | 8.6. |[[#Cycles in Codimension 2, part II|Cycles in Codimension 2, part II]] |N.N. |- | 15.6. |[[#Bloch III: The dilogarithm|Bloch III: The dilogarithm]] |N.N. |- | 22.6. |[[#The five term relation and K-theory|The five term relation and K-theory]] |N.N. |- | 29.6. |[[#The dilog, scissors congruences and volumes of hyperbolic spaces|The dilog, scissors congruences and volumes of hyperbolic spaces]] |N.N. |- | 6.7. |[[#The dilog and zeta functions|The dilog and zeta functions]] |N.N. |- | 13.7. |[[#The dilog in physics|The dilog in physics]] |Wendland/Scheidegger ? |- | 20.7. |[[#Outlook: Mixed motives and periods|Outlook: Mixed motives and periods]] |Huber/Hörmann |} = Introduction = Motivation for alg. K-Theory (also talking briefly about top. K-Theory) = Cech cohomology and the Hodge conjecture in codim 1 = Definition of vector bundles by Cech cocycles - Weibel, p. 54 ff. I.5.10 = Chow groups and Chern classes = The classical construction of Chow groups and the Chern classes using the splitting principle. = Elementary algebraic K-Theory: K0 and K1 = Also the relation of algebraic K_0 with the gamma-filtration on K_0 ? References: <ref name="Mil71"/> <ref name="Wei13"/> Weibel II, §8 = Elementary algebraic K-Theory: K2 = References: <ref name="Mil71"/> <ref name="Wei13"/> Weibel, III = Cycles in Codimension 2, part I = References: <ref name="Blo74"/>, (<ref name="Blo10"/>, §4) = Cycles in Codimension 2, part II = References: <ref name="Blo74"/>, (<ref name="Blo10"/>, §4) = The dilogarithm and a generalization of the exponential sequence = Introduction of the dilogarithm by integration, its power series and then a survey of Bloch's article '78 References: <ref name="Blo78"/>, (<ref name="Blo10"/>, §6) Reference for the Dilogarithm: <ref name="Zag07"/> = The five term relation of the dilogarithm = References: <ref name="Blo00"/>, in particular 7.4 and all what is needed from before There should/could be some overlap with the following talk; speakers should coordinate = The dilog, scissors congruences and volumes of hyperbolic spaces = References: <ref name="DS83"/>, <ref name="Gon99"/> = The dilog and zeta functions = References: <ref name="Blo00"/>, (<ref name="Zag07"/>, I, §5) = The dilog in physics = Starting point: The quantum dilogarithm (<ref name="Zag07"/>, I D, § 3) = Mixed motives and periods = Historical overview about the developments in the last 35 years... Overview about mixed motives via their realizations and comparison encoding periods. Explain that the dilog appears as a period. Relation between Extensions of Tate-motives and K-theory. Connection with the topics discussed in the seminar. References: <ref name="Lev05"/>, <ref name="BD94"/> = References = <references> <ref name="Blo74">Bloch, S.; ''<math>K_2</math> and algebraic cycles''. Ann. of Math. (2) 99 (1974), 349–379. </ref> <ref name="Blo00">Bloch, S.; ''Higher regulators, algebraic K-theory, and zeta functions of elliptic curves''. CRM Monograph Series, 11. American Mathematical Society, Providence, RI, 2000. x+97 pp.</ref> <ref name="Blo78">Bloch, S.; ''Applications of the dilogarithm function in algebraic K-theory and algebraic geometry''. Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), pp. 103–114, Kinokuniya Book Store, Tokyo, 1978.</ref> <ref name="Blo10">Bloch, S.; ''Lectures on algebraic cycles''. Second edition. New Mathematical Monographs, 16. Cambridge University Press, Cambridge, 2010. xxiv+130 pp.</ref> <ref name="Blo81">Bloch, S.; ''The dilogarithm and extensions of Lie algebras''. Algebraic K-theory, Evanston 1980 (Proc. Conf., Northwestern Univ., Evanston, Ill., 1980), pp. 1–23, Lecture Notes in Math., 854, Springer, Berlin-New York, 1981. </ref> <ref name="Zag07">Zagier, D.; ''The dilogarithm function''. Frontiers in number theory, physics, and geometry. II, 3–65, Springer, Berlin, 2007. </ref> <ref name="Hut13">Hutchinson, K.; ''A Bloch-Wigner complex for <math>\mathrm{SL}_2</math>''. J. K-Theory 12 (2013), no. 1, 15–68. </ref> <ref name="Goe07">Goette, S.; Zickert, Ch.; ''The extended Bloch group and the Cheeger-Chern-Simons class''. Geom. Topol. 11 (2007), 1623–1635. </ref> <ref name="Gon95">Goncharov, A. B.; ''Geometry of configurations, polylogarithms, and motivic cohomology''. Adv. Math. 114 (1995), no. 2, 197–318. </ref> <ref name="Lew81">Lewin, L.; ''Polylogarithms and associated functions''. With a foreword by A. J. Van der Poorten. North-Holland Publishing Co., New York-Amsterdam, 1981. xvii+359 pp. </ref> <ref name="Mil71">Milnor, J., ''Introduction to algebraic K-theory''. Annals of Mathematics Studies, No. 72. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. xiii+184 pp. </ref> <ref name="Wei13">Weibel, Ch. A.; ''The K-book. An introduction to algebraic K-theory''. Graduate Studies in Mathematics, 145. American Mathematical Society, Providence, RI, 2013. xii+618 pp. </ref> <ref name="Sus84">Suslin, A. A.; ''Homology of <math>\mathrm{GL}_n</math>, characteristic classes and Milnor K-theory''. Algebraic K-theory, number theory, geometry and analysis (Bielefeld, 1982), 357–375, Lecture Notes in Math., 1046, Springer, Berlin, 1984. </ref> <ref name="Sus91">Suslin, A. A.; ''<math>K_3</math> of a field, and the Bloch group.'' (Russian) Translated in Proc. Steklov Inst. Math. 1991, no. 4, 217–239. Galois theory, rings, algebraic groups and their applications (Russian). </ref> <ref name="Sus87">Suslin, A. A.; ''Algebraic K-theory of fields''. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 222–244, Amer. Math. Soc., Providence, RI, 1987. </ref> <ref name="Zic15">Zickert, Ch. K.; ''The extended Bloch group and algebraic K-theory''. J. Reine Angew. Math. 704 (2015), 21–54. </ref> <ref name="Lev05">Levine, Marc; ''Mixed motives''. Handbook of K-theory. Vol. 1, 2, 429–521, Springer, Berlin, 2005.</ref> <ref name="Blo91"> Bloch, S.; ''Function theory of polylogarithms''. Structural properties of polylogarithms, 275–285, Math. Surveys Monogr., 37, Amer. Math. Soc., Providence, RI, 1991.</ref> <ref name="DS83">Dupont, J. L.; Sah, C. H.; ''Scissors congruences. II''. J. Pure Appl. Algebra, 25(2):159–195, 1982.</ref> <ref name="Gon99">Goncharov, A.; ''Volumes of hyperbolic manifolds and mixed Tate motives''. J. Amer. Math. Soc. 12 (1999), no. 2, 569–618. </ref> <ref name="BD94">Beĭlinson, A.; Deligne, P. ''Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs''. Motives (Seattle, WA, 1991), 97–121, Proc. Sympos. Pure Math., 55, Part 2, Amer. Math. Soc., Providence, RI, 1994. </ref> </references>
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