added the second recording of Peter Arndt’s talk last week, here
]]>added pointer to
Peter Arndt, Abstract motivic homotopy theory, thesis 2017 (web, pdf)
also: lecture at Geometry in Modal HoTT, 2019 (recording I)
The recording of the second talk will become available later today; will update then.
]]>added publication data for
I thought there was room to state the main definition here (this Def.) more clearly, by saying more explicitly what it means to localize “over a site equipped with an interval”.
It used to say:
The motivic homotopy category over is the homotopy localization of the (∞,1)-topos of (∞,1)-sheaves on the Nisnevich site equipped with the interval object .
Now I made it say:
The motivic homotopy category over is the homotopy localization at the affine line (1) of the (∞,1)-topos of (∞,1)-sheaves on the Nisnevich site .
and the link “at the” points to an actual definition of what this means.
]]>added the following reference: Motivic Homotopy Theory: Lectures at a Summer School in Nordfjordeid, Norway, August 2002
]]>I have moved the subsections on algebraic K-theory and algebraic cobordism to the pages algebraic K-theory spectrum and algebraic cobordism, respectively.
]]>I added the reference
I have added to the entry anchors to the definition of and and cross-links back to these definitions, to make it easier for the reader to jump into the middle of this entry and still know what the notation means.
]]>I wrote something about Euler classes and splittings of vector bundles.
]]>I wrote something about A1-coverings and added the statement of Morel’s connectivity theorem at A1-Postnikov filtration.
Did look at it right now after all. One tiny comment: the link labeled “symmetric space” but pointing to bilinear form should go with a bit more of a comment, since there is also symmetric space.
Sorry, I hadn’t noticed. I replaced “symmetric space” with “symmetric bilinear form”.
]]>Did look at it right now after all. One tiny comment: the link labeled “symmetric space” but pointing to bilinear form should go with a bit more of a comment, since there is also symmetric space.
]]>Thanks, Marc, for all the work! Glad that you are looking into these Lab entries on motivic stuff.
(I’ll read your aditions later, can’t right now…)
]]>I added a few sentences about the relation to the theory of symmetric bilinear forms.
]]>I wrote something about the six operations.
]]>I wrote something about realization functors.
]]>I added descriptions of the slice filtration and the -Postnikov filtration at motivic homotopy theory.
]]>Created motivic homotopy theory (renamed from A1-homotopy theory).
Still many blanks to fill in…
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