On The Morel Structure Conjecture

2026/07/09 by Giacomo Bertizzolo · 2 voices
Mathematics · #math.KT #math.AG #math.AT

paper · pdf

Abstract

We prove that Witt K-theory is effective over any perfect field of characteristic 2 and consequently finish the proof of the Morel structure conjecture initiated by Bachmann.

Citations

• Strongly A¹-invariant sheaves (after F. Morel)
• A motivic spectrum representing hermitian K-theory
• Motivic cohomology of equicharacteristic schemes
• Milnor-Witt K-theory and Witt K-theory of a field
• Notes on Milnor-Witt K-theory
• Milnor-Witt Motives
• The Generalized Slices of Hermitian K-Theory
• Milnor-Witt K-groups of local rings
• Slices of hermitian K–theory and Milnor’s conjecture on quadratic forms
• A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula
• From algebraic cobordism to motivic cohomology
• The homotopy coniveau tower
• An exact sequence for K∗M∕2 with applications to quadratic forms

Discussions

• Giacomo Bertizzolo On The Morel Structure Conjecture https://arxiv.org/abs/2607.08905 [bsky, 0 points, 0 comments]
• Giacomo Bertizzolo: On The Morel Structure Conjecture https://arxiv.org/abs/2607.08905 https://arxiv.org/pdf/2607.08905 https://arxiv.org/html/2607.08905 [bsky, 0 points, 0 comments]

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• Milnor-Witt K-theory and Witt K-theory of a field
• Tautological characteristic classes II: the Witt class
• Stabilization of the Witt group
• On the algebraic K-theory of Witt vectors of finite length
• The Witt construction in characteristic one and Quantization