A UNIVERSALITY THEOREM FOR VOEVODSKY'S ALGEBRAIC COBORDISM SPECTRUM

By Ivan Panin, K. Pimenov, O. Rondigs. 2007

67 citations recorded by the source corpus.

An algebraic version of a theorem of Quillen is proved. More precisely, for a regular Noetherian scheme S of finite Krull dimension, we consider the motivic stable homotopy category SH(S) of P 1 -spectra, equipped with the symmetric monoidal structure described in [7]. The algebraic cobordism P 1 -spectrum MGL is considered as a commutative monoid equipped with a canonical orientation th MGL 2 MGL 2,1 (Th(O(i1))). For a commutative monoid E in the category SH(S), it is proved that the assignment ’ 7! ’(th MGL ) identifies the set of monoid homomorphisms ’: MGL ! E in the motivic stable homotopy category SH(S) with the set of all orientations of E. This result generalizes a result of G. Vezzosi in [12].

View Paper: https://www.semanticscholar.org/paper/5a6deb82a3556fe3a938f824dd61bf902f66b2f6

How researchers see this paper

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

Citations in the corpus

On the motivic spectra representing algebraic cobordism and algebraic $K$-theory (2007, background): “See Adams [1] and Panin-Pimenov-Röndigs [23] for details.”
The motivic adams spectral sequence (2009, background): “This is constructed as a motivic symmetric ring spectrum in [ PPR , Section 2.1].”
The special fiber of the motivic deformation of the stable homotopy category is algebraic (2018, background): “Let MGL be the motivic algebraic cobordism spectrum introduced by Voevodsky [63] and studied by Levine-Morel [33], Panin-Pimenov-Röndigs [49] and many others.”