Ryomei Iwasa - 1/3 Motivic Stable Homotopy Theory
Автор: Institut des Hautes Etudes Scientifiques (IHES)
Загружено: 2023-07-18
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Описание:
In joint work with Toni Annala and Marc Hoyois, we have developed motivic stable homotopy in broader generality than the theory initiated by Voevodsky, so that non-𝐴1-invariant theories can also be captured. I’ll describe this, bearing in mind its connection to algebraic K-theory and p-adic cohomology such as syntomic cohomology. The course is divided roughly into three parts.
Foundations: The goal of this part is to grasp the notion of 𝑃1-spectrum, which forms the basic framework of motivic stable homotopy theory.
Techniques: The goal of this part is to understand our main technique, P-homotopy invariance, which allows us to do a homotopy theory in algebraic geometry while keeping the affine line 𝐴1 non-contractible.
Applications: In this part, we apply our motivic homotopy theory to algebraic K-theory of arbitrary qcqs schemes, and prove an algebraic analogue of Snaith theorem, which says that K-theory is obtained from the Picard stack by inverting the Bott element.
Ryomei Iwasa (Université Paris-Saclay)
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