Noncommutative L-Functions for Varieties over Finite Fields

Malte Witte

Type: Book-Chapter

Publication Date: 2014-01-01

Citations: 2

DOI: https://doi.org/10.1007/978-3-642-55245-8_15

Abstract

We consider certain perfect complexes of adic sheaves on varieties over finite fields that take values in modules over noncommutative rings Λ. To each such complex we associate an L-function living in the first $$\mathop{\text{K}}\nolimits$$ -group of the power series ring over Λ. We then show that these L-functions satisfy a suitably generalised multiplicative Grothendieck trace formula.

Locations

Contributions in mathematical and computational sciences - View
arXiv (Cornell University) - View - PDF
Publikationsserver der Universität Regensburg (Uni Regensburg) - View - PDF

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Works Cited by This (27)

Action	Title	Year	Authors
+	Whitehead Groups of Finite Groups	1988	Robert Oliver
+	K-Theory and Noncommutative Geometry	2008	Guillermo Cortiñas⋆ Joachim Cuntz Max Karoubi Ryszard Nest Charles A. Weibel
+	Cohomologie l-adique et fonctions L	1977	Alexandre Grothendieck Iléana Bucur
+	Cohomology of Number Fields	2008	Jürgen Neukirch Alexander Schmidt Kay Wingberg
+ PDF Chat	Théorie des Topos et Cohomologie Etale des Schémas	1972	J. L. Verdier B. Saint-Donat Alexandre Grothendieck J.-L. Verdier
+	Unit L-functions for \'etale sheaves of modules over noncommutative rings	2013	Malte Witte
+	The 1-type of a Waldhausen K-theory spectrum	2007	Fernando Muro Andrew Tonks
+	�ber gewisse Galoiscohomologiegruppen	1979	Peter Schneider
+	K_1 of a p-adic group ring II. The determinantal kernel SK_1	2013	Ted Chinburg G. Pappas M. J. Taylor
+ PDF Chat	Unit L-Functions and a Conjecture of Katz	2001	Matthew Emerton Mark Kisin