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Category Archives: Uncategorized
The stable cohomology of SL(F_p)
Back by popular demand: an actual mathematics post! Today’s problem is the following: compute the cohomology of for a (modp) algebraic representation. Step 0 is to say what this problem actually is. It makes sense to talk about certain algebraic … Continue reading
Posted in Mathematics, Uncategorized
Tagged completed cohomology, completed Ktheory, Eric Friedlander, Evens, Ktheory, stable cohomology
3 Comments
Referee Requests
################################################### From: Mathematics Editorial Office Subject: [Mathematics] Review Request Date: December 26, 2018 at 7:43:31 AM CST Dear Professor Calegari, Happy new year. We have received the following manuscript to be considered for publication in Mathematics (http://www.mdpi.com/journal/mathematics/) and kindly invite … Continue reading
Posted in Mathematics, Rant, Uncategorized
Tagged Elsevier, MPDI, Predatory Journals, Reviewing Scam
7 Comments
Localglobal compatibility for imaginary quadratic fields
One of the key steps in the 10author paper is to prove results on localglobal compatibility for Galois representations associated to torsion classes. The results proved in that paper, unfortunately, fall wellshort of the optimal desired localglobal compatibility statement, because … Continue reading
JacquetLanglands and an old R=T conjecture
This is part 2 of a series of posts on R=T conjectures for inner forms of GL(2). (See here for part 1). (Edit: this is still incorrect and there should have been a part 3, but I’ve been distracted… in … Continue reading
JacquetLanglands and a new R=T conjecture
It is somewhat mysterious how one should formulate the JacquetLanglands correspondence integrally, particularly in the presence of torsion classes. Even the classical case has many subtleties including for example some results in this paper of Ribet. In the case of … Continue reading
Posted in Uncategorized
Tagged Akshay Venkatesh, Allen Cheng, David Helm, I have a subtle plan my lord, JacquetLanglands, Jeff Manning, Ken Ribet, R=T, torsion
4 Comments
A strange continuity
Returning to matters OPAQUE, here is the following problem which may well now be approachable by known methods. Let me phrase the conjecture in the case when the prime p = 2 and the level N = 1. As we … Continue reading
Posted in Uncategorized
Tagged Eigencurve, Galois Representations, Halo, Kevin Buzzard, Lloyd Kilford, OPAQUE, Robert Coleman
2 Comments
Irregular Lifts, Part II
This is the global counterpart to the last post. I was going to write this post in a more general setting, but the annoyances of general reductive groups got the better of me. Suppose we fix the following: A number … Continue reading
Posted in Uncategorized
Tagged Artin Conjecture, Galois Representations, HodgeTate, lifting, On the record
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