Reduced power operations in motivic cohomology

By Vladimir Voevodsky. 2001

340 citations recorded by the source corpus.

In this paper we construct an analog of Steenrod operations in motivic cohomology and prove their basic properties including the Cartan formula, the Adem relations and the realtions to characteristic classes.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d7cabe9d91fad1d676de8a2acd96cc4c457d5946

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Daniel Dugger
2. Daniel Isaksen
3. A. Vishik
4. P. Ostvaer
5. O. Rondigs
6. K. Ormsby
7. J. Heller
8. Markus Spitzweck

In Geometry and Topology

1. Daniel Isaksen
2. M. Levine
3. Daniel Dugger
4. Markus Spitzweck
5. O. Rondigs
6. P. Ostvaer
7. K. Ormsby
8. J. Heller

In Mathematical Physics

1. Daniel Isaksen
2. M. Levine
3. Daniel Dugger
4. Markus Spitzweck
5. P. Ostvaer
6. K. Ormsby
7. O. Rondigs
8. J. Heller

Citations in the corpus

• Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms (2013, methodology): “When the base scheme is a field of characteristic zero, these identifications follow from Voevodsky’s work on the motivic Steenrod algebra [62], while the generalization to our set-up relies on [18].”
• On motivic cohomology with Z/l -coefficients (2008, background): “The symmetric group Si acts by permutations on M⊗i.”
• The motivic adams spectral sequence (2009, methodology): “H / with the dual Steenrod algebra A as computed by Voevodsky in [32].”
• Stable Stems (2014, background): “The (dual) motivic Steenrod algebra over C is [44] [42] [7, Section 5.”
• Convergence of the Motivic Adams Spectral Sequence (2011, background): “Let X be a k-connective motivic cell spectrum of finite type.”
• On the Chow groups of quadratic Grassmannians (2005, methodology): “Voevodsky in the context of arbitrary motivic cohomology - see [13], and then a simpler construction was given by P.”
• Low-dimensional Milnor–Witt stems over ℝ (2015, background): “The pair (M2,A∗) is a Hopf algebroid; recall from [Voevodsky 2003] (see also [Borghesi 2007; Hoyois et al. 2013; Riou 2012]) that this structure is described by A∗ =M2[τ0, τ1, . . . , ξ0, ξ1, . . . ]/(ξ0 = 1, τ 2k = τξk+1+ ρτk+1+ ρτ0ξk+1), ηL(τ )= τ, ηR(τ )= τ + ρτ0, ηL(ρ)= ηR(ρ)= ρ, 1(τk)= τk ⊗ 1+…”
• Steenrod operations in chow theory (2003, background): “Although the details of his construction have not yet fully appeared, these operations should agree with ours and, over a field where motivic Date: October 17, 1999.”
• The congruence criterion for power operations in Morava $E$-theory (2009, background): “notion as well as various generalizations have been much studied in the literature on Hopf algebras and allied notions. It has entered topology in various guises. I first learned about the notion from [Voe03]; the motivic Steenrod algebra is naturally a twisted bialgebra over the motivic homology of ”
• Motivic cohomology with Z/2-coefficients (2003, methodology): “In the former case the result follows from Lemma 6.8 and again [ 42, Theorem 2.4 ].”