Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

Frobenius line invariance of algebraic $ K$-theory


Author: Oliver Braunling
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 19F27, 14F30
DOI: https://doi.org/10.1090/tran/8231
Published electronically: August 28, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The $ K$-theory of smooth schemes is $ \mathbf {A}^{1}$-invariant. We show that this remains true over finite fields if one replaces the affine line by the Frobenius line, i.e., the non-commutative algebra where multiplication with the variable behaves like the Frobenius. Emerton had shown that over regular rings the Frobenius line is left coherent. As a technical ingredient for our theorem, but also of independent interest, we extend this and show that merely assuming finite type (or just $ F$-finite), the Frobenius line is right coherent.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 19F27, 14F30

Retrieve articles in all journals with MSC (2010): 19F27, 14F30


Additional Information

Oliver Braunling
Affiliation: Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, D-79104 Freiburg im Breisgau, Germany

DOI: https://doi.org/10.1090/tran/8231
Received by editor(s): March 7, 2018
Received by editor(s) in revised form: October 10, 2019, and April 10, 2020
Published electronically: August 28, 2020
Additional Notes: The author was supported by the GK1821 “Cohomological Methods in Geometry”and the Freiburg Institute for Advanced Studies (FRIAS)
Article copyright: © Copyright 2020 American Mathematical Society