scholarly journals Some Recent Trends in Motivic Homotopy Theory

2020 ◽  
Vol 67 (01) ◽  
pp. 1
Author(s):  
Marc Levine
Keyword(s):  
Homotopy Theory ◽  
Motivic Homotopy Theory ◽  
Recent Trends ◽  
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

Motivic Homotopy Theory

2008 ◽  
Vol 76 (1) ◽  
pp. 165-199 ◽  
Author(s):  
Marc Levine
Keyword(s):  
Homotopy Theory ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy
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