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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Quaternionic algebraic cycles and reality
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by Pedro F. dos Santos and Paulo Lima-Filho PDF
Trans. Amer. Math. Soc. 356 (2004), 4701-4736 Request permission

Abstract:

In this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real Brauer-Severi varieties, under the action of the Galois group $Gal({\mathbb C} / {\mathbb R})$. Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymour’s quaternionic $K$-theory, and the other one classifies an equivariant cohomology theory ${\mathfrak Z}^*(-)$ which is a natural recipient of characteristic classes $KH^*(X) \to {\mathfrak Z}^*(X)$ for quaternionic bundles over Real spaces $X$.
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Additional Information
  • Pedro F. dos Santos
  • Affiliation: Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal
  • Email: pedfs@math.ist.utl.pt
  • Paulo Lima-Filho
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • Email: plfilho@math.tamu.edu
  • Received by editor(s): October 9, 2001
  • Published electronically: June 22, 2004
  • Additional Notes: The first author was supported in part by FCT (Portugal) through program POCTI and grant POCTI/1999/MAT/34015. The second author was partially supported by the NSF
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 4701-4736
  • MSC (2000): Primary 55P91; Secondary 19L47, 14C25
  • DOI: https://doi.org/10.1090/S0002-9947-04-03663-3
  • MathSciNet review: 2084395