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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 6th 2020
   • (edited Dec 6th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexam giving this theorem its own little entry, for ease of cross-linking relevant other entries, such as _[[Todd class]]_, _[[chern character]]_, _[[Thom class]]_ <a href="https://ncatlab.org/nlab/revision/rational+Todd+class+is+Chern+character+of+Thom+class/1">v1</a>, <a href="https://ncatlab.org/nlab/show/rational+Todd+class+is+Chern+character+of+Thom+class">current</a>

   am giving this theorem its own little entry, for ease of cross-linking relevant other entries, such as Todd class, chern character, Thom class

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 12th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * [[Larry Smith]], Section 1 of: _The Todd character and the integrality theorem for the Chern character_, Illinois J. Math. Volume 17, Issue 2 (1973), 301-310 ([euclid:ijm/1256051760](https://projecteuclid.org/euclid.ijm/1256051760)) which has the statement at the level of representing ring spectra <a href="https://ncatlab.org/nlab/revision/diff/rational+Todd+class+is+Chern+character+of+Thom+class/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+Todd+class+is+Chern+character+of+Thom+class/2">v2</a>, <a href="https://ncatlab.org/nlab/show/rational+Todd+class+is+Chern+character+of+Thom+class">current</a>

   added pointer to

   • Larry Smith, Section 1 of: The Todd character and the integrality theorem for the Chern character, Illinois J. Math. Volume 17, Issue 2 (1973), 301-310 (euclid:ijm/1256051760)

   which has the statement at the level of representing ring spectra

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 18th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded now also a brief remark on statement from [Smith 73](https://ncatlab.org/nlab/show/rational+Todd+class+is+Chern+character+of+Thom+class#Smith73) at the level of representing morphisms of ring spectra: $$ Td \;\colon\; M \mathrm{U} \overset{ \sigma^{KU} }{\longrightarrow} KU \overset{ ch }{\longrightarrow} H^{ev}\mathbb{Q} $$ (changing Smith's notation just a little, since "th" seems a bad abbreviation for "Todd", especially here where _Thom_ classes play a key role). This is a most neat perspective. Does any other author discuss this? I have trouble finding any mentioning of this after Smith's note back from 1973 <a href="https://ncatlab.org/nlab/revision/diff/rational+Todd+class+is+Chern+character+of+Thom+class/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+Todd+class+is+Chern+character+of+Thom+class/4">v4</a>, <a href="https://ncatlab.org/nlab/show/rational+Todd+class+is+Chern+character+of+Thom+class">current</a>

   added now also a brief remark on statement from Smith 73 at the level of representing morphisms of ring spectra:

   $$Td \;\colon\; M \mathrm{U} \overset{ \sigma^{KU} }{\longrightarrow} KU \overset{ ch }{\longrightarrow} H^{ev}\mathbb{Q}$$

   (changing Smith’s notation just a little, since “th” seems a bad abbreviation for “Todd”, especially here where Thom classes play a key role).

   This is a most neat perspective. Does any other author discuss this? I have trouble finding any mentioning of this after Smith’s note back from 1973

   diff, v4, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 18th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI see that in * Matthias Jonas Spiegel, Section 2.3.2 of _K-Theory of Intersection Spaces_, 2013 ([doi:10.11588/heidok.00015738](https://doi.org/10.11588/heidok.00015738)) the reference given for the statement is still Smith 73 and nothing else. <a href="https://ncatlab.org/nlab/revision/diff/rational+Todd+class+is+Chern+character+of+Thom+class/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+Todd+class+is+Chern+character+of+Thom+class/5">v5</a>, <a href="https://ncatlab.org/nlab/show/rational+Todd+class+is+Chern+character+of+Thom+class">current</a>

   I see that in

   • Matthias Jonas Spiegel, Section 2.3.2 of K-Theory of Intersection Spaces, 2013 (doi:10.11588/heidok.00015738)

   the reference given for the statement is still Smith 73 and nothing else.

   diff, v5, current