Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the $K$-theory and topological cyclic homology of smooth schemes over a discrete valuation ring
HTML articles powered by AMS MathViewer

by Thomas Geisser and Lars Hesselholt PDF
Trans. Amer. Math. Soc. 358 (2006), 131-145 Request permission


We show that for a smooth and proper scheme over a henselian discrete valuation ring of mixed characteristic $(0,p)$, the $p$-adic étale $K$-theory and $p$-adic topological cyclic homology agree.
  • Ofer Gabber, $K$-theory of Henselian local rings and Henselian pairs, Algebraic $K$-theory, commutative algebra, and algebraic geometry (Santa Margherita Ligure, 1989) Contemp. Math., vol. 126, Amer. Math. Soc., Providence, RI, 1992, pp. 59–70. MR 1156502, DOI 10.1090/conm/126/00509
  • Thomas Geisser and Lars Hesselholt, Topological cyclic homology of schemes, Algebraic $K$-theory (Seattle, WA, 1997) Proc. Sympos. Pure Math., vol. 67, Amer. Math. Soc., Providence, RI, 1999, pp. 41–87. MR 1743237, DOI 10.1090/pspum/067/1743237
  • Thomas G. Goodwillie, Calculus. I. The first derivative of pseudoisotopy theory, $K$-Theory 4 (1990), no. 1, 1–27. MR 1076523, DOI 10.1007/BF00534191
  • Thomas G. Goodwillie, Calculus. II. Analytic functors, $K$-Theory 5 (1991/92), no. 4, 295–332. MR 1162445, DOI 10.1007/BF00535644
  • Lars Hesselholt, Stable topological cyclic homology is topological Hochschild homology, Astérisque 226 (1994), 8–9, 175–192. $K$-theory (Strasbourg, 1992). MR 1317119
  • L. Hesselholt and I. Madsen, On the $K$-theory of local fields, Ann. of Math. 158 (2003), 1–113.
  • J. Peter May, Simplicial objects in algebraic topology, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992. Reprint of the 1967 original. MR 1206474
  • Randy McCarthy, Relative algebraic $K$-theory and topological cyclic homology, Acta Math. 179 (1997), no. 2, 197–222. MR 1607555, DOI 10.1007/BF02392743
  • I. A. Panin, The Hurewicz theorem and $K$-theory of complete discrete valuation rings, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), no. 4, 763–775, 878 (Russian). MR 864175
  • A. A. Suslin, Stability in algebraic $K$-theory, Algebraic $K$-theory, Part I (Oberwolfach, 1980) Lecture Notes in Math., vol. 966, Springer, Berlin, 1982, pp. 304–333. MR 689381, DOI 10.1007/BFb0062181
  • Andrei A. Suslin, On the $K$-theory of local fields, Proceedings of the Luminy conference on algebraic $K$-theory (Luminy, 1983), 1984, pp. 301–318. MR 772065, DOI 10.1016/0022-4049(84)90043-4
  • R. W. Thomason, Algebraic $K$-theory and étale cohomology, Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 3, 437–552. MR 826102
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11G25, 19F27
  • Retrieve articles in all journals with MSC (2000): 11G25, 19F27
Additional Information
  • Thomas Geisser
  • Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
  • Email:
  • Lars Hesselholt
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 329414
  • Email:
  • Received by editor(s): August 15, 2002
  • Received by editor(s) in revised form: January 2, 2004
  • Published electronically: December 28, 2004
  • Additional Notes: Both authors were supported in part by the NSF and the Alfred P. Sloan Foundation. The first author received additional support from the JSPS
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 131-145
  • MSC (2000): Primary 11G25; Secondary 19F27
  • DOI:
  • MathSciNet review: 2171226