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bio website math.jhu.edu/~beardsle
location Baltimore, MD
age 27
visits member for 4 years
seen 19 hours ago

Learning.


Dec
16
comment textbooks on modern algebraic geometry for 21st-century starters
I might add that without a good understanding of homological algebra, really important concepts like sheaf cohomology and derived functors aren't going to make much sense. For that, I strongly recommend Charles Weibel's book. It's encyclopedic and well written. The only drawback is that some of his terminology is non-standard.
Dec
16
comment textbooks on modern algebraic geometry for 21st-century starters
Ultimately, it really really really depends on what you want to do. You may be the sort of person who can just start memorizing a lot of terminology and abstract nonsense, but if you have no intuition for what a scheme is, you're unlikely to be able to prove very much about schemes. On the other hand, I came from topology, and it was very useful for me to be able to just thing about a stack from the category theory perspective. So it might be worth it to provide some context in your question.
Dec
16
comment Coaction of a group
Generally if a group $G$ acts on a ring $A$ then there is a coaction $A\to C(G)\otimes A$. In other words, the dual of the group ring is a Hopf-algebra and coacts on the thing that $A$ acts on.
Dec
16
comment Coaction of a group
Do you mean to write "naturally induced coaction" or something? What do you want to have naturally induced on $A\otimes C(G)$?
Dec
13
awarded  Yearling
Dec
8
awarded  Announcer
Dec
8
comment Uniqueness of Complex Orientation of Morava K-theory
Wow @Neil this is an incredible answer. Thank you so much. It seems surprising to me that every FGL over $K(n)_\ast$ induces a map of ring spectra $MU\to K(n)$. This cannot be true for complex orientations in general, can it? In other words, for a ring spectrum R it is not the case that an FGL on $R_\ast$ induces a complex orientation on $R$.
Dec
8
accepted Uniqueness of Complex Orientation of Morava K-theory
Dec
6
asked Uniqueness of Complex Orientation of Morava K-theory
Dec
2
awarded  Nice Question
Dec
1
revised Thom Spectra and Hopf-Galois Extensions of Ring Spectra
fixed a minor error in notation
Nov
30
accepted Thom isomorphism from the ABGHR perspective
Nov
30
comment Thom isomorphism from the ABGHR perspective
Does that spectrum map you describe, $Mf\to R$ need to be multiplicative?
Nov
30
accepted Cohomology of Formal Groups
Nov
30
accepted Hopf-algebras in associative ring spectra
Nov
30
revised Hopf-algebras in associative ring spectra
deleted 85 characters in body
Nov
30
revised Thom isomorphism from the ABGHR perspective
added 76 characters in body
Nov
30
revised Thom isomorphism from the ABGHR perspective
added 1 character in body
Nov
30
asked Thom isomorphism from the ABGHR perspective
Nov
17
comment Hopf-algebras in associative ring spectra
Actually this answer is rife with mistakes and misunderstandings. I'll try to update it soon...