Motivic Homotopy Theory and Refined Enumerative Geometry

2020 ◽  
Keyword(s):  
Homotopy Theory ◽  
Enumerative Geometry ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy

Rigidity in motivic homotopy theory

2008 ◽  
Vol 341 (3) ◽  
pp. 651-675 ◽  
Author(s):  
Oliver Röndigs ◽  
Paul Arne Østvær
Keyword(s):  
Homotopy Theory ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy

scholarly journals THE TOM DIECK SPLITTING THEOREM IN EQUIVARIANT MOTIVIC HOMOTOPY THEORY

2021 ◽  
pp. 1-70
Author(s):  
DAVID GEPNER ◽  
JEREMIAH HELLER
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Fixed Points ◽  
Homotopy Theory ◽  
Independent Interest ◽  
Splitting Theorem ◽  
Motivic Homotopy Theory ◽  
Group A ◽  
Motivic Homotopy ◽  
A Finite Group

Abstract We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck’s splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and constructions for equivariant motivic homotopy theory of independent interest. This includes geometric fixed-point functors and the motivic Adams isomorphism.

scholarly journals Primes and fields in stable motivic homotopy theory

2018 ◽  
Vol 22 (4) ◽  
pp. 2187-2218 ◽  
Author(s):  
Jeremiah Heller ◽  
Kyle Ormsby
Keyword(s):  
Homotopy Theory ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy

scholarly journals Dimensional homotopy t-structures in motivic homotopy theory

2017 ◽  
Vol 311 ◽  
pp. 91-189 ◽  
Author(s):  
Mikhail Bondarko ◽  
Frédéric Déglise
Keyword(s):  
Homotopy Theory ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy

scholarly journals THE ZEROTH -STABLE HOMOTOPY SHEAF OF A MOTIVIC SPACE

2021 ◽  
pp. 1-25
Author(s):  
Tom Bachmann
Keyword(s):  
Homotopy Theory ◽  
Stable Homotopy ◽  
Main Conjecture ◽  
Homotopy Invariant ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy

Abstract We establish a kind of ‘degree $0$ Freudenthal ${\mathbb {G}_m}$ -suspension theorem’ in motivic homotopy theory. From this we deduce results about the conservativity of the $\mathbb P^1$ -stabilization functor. In order to establish these results, we show how to compute certain pullbacks in the cohomology of a strictly homotopy-invariant sheaf in terms of the Rost–Schmid complex. This establishes the main conjecture of [2], which easily implies the aforementioned results.

scholarly journals Erratum to: Rigidity in motivic homotopy theory

2011 ◽  
Vol 350 (3) ◽  
pp. 755-756
Author(s):  
Oliver Röndigs ◽  
Paul Arne Østvær
Keyword(s):  
Homotopy Theory ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy

scholarly journals Motivic connective K-theories and the cohomology of A(1)

2011 ◽  
Vol 7 (3) ◽  
pp. 619-661 ◽  
Author(s):  
Daniel C. Isaksen ◽  
Armira Shkembi
Keyword(s):  
Spectral Sequence ◽  
Fixed Points ◽  
Homotopy Theory ◽  
Steenrod Algebra ◽  
The Real ◽  
Special Cases ◽  
Ext Groups ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy ◽  
Homotopy Fixed Points

AbstractWe make some computations in stable motivic homotopy theory over Spec ℂ, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct over ℂ a motivic analogue of the real K-theory spectrum KO. We also establish a theory of motivic connective covers over ℂ to obtain a motivic version of ko. We establish an Adams spectral sequence for computing motivic ko-homology. The E2-term of this spectral sequence involves Ext groups over the subalgebra A(1) of the motivic Steenrod algebra. We make several explicit computations of these E2-terms in interesting special cases.

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