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Faithful readers of Vivastgasse 7 may have noticed that we haven’t posted anything in a while now- the reasons are numerous, but it mostly boils down to the fact that two of us (Anton and I) are in the middle of resolving several quasi-bureaucratic/ quasi-academic things: Anton is right now in Ukraine, finishing up his thesis and busy planning his move to Paris in a couple of months for his first postdoc. I’m busy planning a move as well- off to Durham next month for five months. So both of us are sort of ‘out-of-commission’ right now. However, I do intend to post something soon (maybe this weekend?) either on schemes over the mysterious “field with one element” or better yet, an unpacking of our guest-blogger Sniggy Mahanta’s post on conformal field theories. (Thanks goes to AJ Tolland for pointing out some gross inaccuracies in that post!)

But here is the main reason for this (non-mathematical) post- to vent!

Recently I asked Faltings for some references for a self-study of Arakelov theory beyond Lang’s *Arakelov theory.*

He suggested the following (all revolving around the arithmetic Riemann-Roch theorem):

1. Papers by Gillet and Soule on arithmetic intersection theory

2. Papers by Bismut, Gillet and Soule on determinant of cohomology of an arithmetic variety (towards Riemann-Roch for this determinant.)

Of late, a lot of people have been asking me about Tannakian categories, so I decided to post this short blurb (mainly to check the Latex-related features of wordpress and also to provide some bird’s-eye view of why we should care about Tannakian categories.)

To begin with:

**Definition**

A *neutral Tannakian category * over a base field is a rigid abelian tensor category with an -linear exact faithful tensor* * ( being the category of vector spaces over ) which one calls the *fiber functor*.

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