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Article

An extended version of additive K-theory

  • Stavros Garoufalidis (a1)
Abstract

There are two infinitesimal (i.e., additive) versions of the K-theory of a field F: one introduced by Cathelineau, which is an F-module, and the other introduced by Bloch-Esnault, which is an F*-module. Both versions are equipped with a regulator map, when F is the field of complex numbers.

We will introduce an extended version of Cathelineau's group, and a complex-valued regulator map given by the entropy. We will also give a comparison map between our extended version and Cathelineau's group.

Our results were motivated by two unrelated sources: Neumann's work on the extended Bloch group (which is isomorphic to indecomposable K3 of the complex numbers), and the study of singularities of generating series of hypergeometric multisums.

Copyright
COPYRIGHT: © ISOPP 2009
References
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AD.Aczél, J. and Dhombres, J., Functional equations in several variables, Encyclopedia of Mathematics and its Applications 31 Cambridge University Press, Cambridge, 1989
BD.Beilinson, A. and Deligne, P., Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs, in Motives, Proc. Sympos. Pure Math. 55, Part 2, (1994) 97–121
BE.Bloch, S. and Esnault, H., The additive dilogarithm, in Kazuya Kato's fiftieth birthday. Doc. Math. (2003) Extra Vol. 131–155
Ca1.Cathelineau, J.L., Remarques sur les différentielles des polylogarithmes uniformes, Ann. Inst. Fourier 46 (1996) 1327–1347
Ca2.Cathelineau, J.L., Infinitesimal polylogarithms, multiplicative presentations of Kaehler differentials and Goncharov complexes, talk at the workshop on Polylogarithms, Essen, 05 1–4
Da.Daróczy, Z., Generalized information functions, Information and Control 16 (1970) 36–51
DZ.Dupont, J.L. and Zickert, C., A dilogarithmic formula for the Cheeger-Chern- Simons class, Geom. Topol. 10 (2006) 1347–1372
E-VG.Elbaz-Vincent, P. and Gangl, H., On poly(ana)logs. I, Compositio Math. 130 (2002) 161–210
Ga1.Garoufalidis, S., q-terms, singularities and the extended Bloch group, preprint 2007 arXiv:0708.0018
Ga2.Garoufalidis, S., An ansatz for the asymptotics of hypergeometric multisums, Adv. Applied Math., in press
GZ.Goette, S. and Zickert, C., The Extended Bloch Group and the Cheeger-Chern- Simons Class, Geom. Topol. 11 (2007) 1623–1635
O.Olver, F., Asymptotics and special functions, Reprint. AKP Classics. A K Peters, Ltd., Wellesley, MA, 1997
Ne.Neuman, W.D., Extended Bloch group and the Cheeger-Chern-Simons class, Geom. Topol. 8 (2004) 413–474
Za.Zagier, D., Polylogarithms, Dedekind zeta functions and the algebraic K-theory of fields, in Arithmetic algebraic geometry, Progr. Math. 89 (1991) 391–430
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Journal of K-Theory
  • ISSN: 1865-2433
  • EISSN: 1865-5394
  • URL: /core/journals/journal-of-k-theory
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