### About this blog

Rigorous trivialities is a web log about mathematics, but especially geometry, broadly construed. Contributors will be Charles Siegel, Jim Stankewicz and occasionally Matt Deland. Charles specializes in algebraic geometry, topology and mathematical physics. Jim specializes in arithmetic algebraic geometry. Matt has transitioned from algebraic geometry to work in industry.

Header is taken from the larger work by fdecomite under the creative commons license.

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# Monthly Archives: September 2009

## B-N-R Part 5: Spectral Curves

Today we’re back to some material from the first post in this series, and going to prove an actual theorem about vector bundles. Next time, we’ll be getting into the heart of the paper, and that may be my last … Continue reading

Posted in Abelian Varieties, Big Theorems, Curves, Vector Bundles
4 Comments

## Blogroll Update Day

I’ve been a lot more active recently, now that my life has quieted down a bit into reading papers, running seminars, taking classes, and teaching a bit, instead of the craziness of a wedding. So now, something I’ve been meaning … Continue reading

Posted in Uncategorized
3 Comments

## B-N-R Part 4: Prym Varieties

The last post was on the generalities of Abelian varieties, and constructing a map. This time, we’re going to do it for a specific one, and the maps involved will all be useful later. We start out with a finite … Continue reading

Posted in Abelian Varieties, Big Theorems, Curves, Vector Bundles
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## B-N-R Part 3: PPAV’s and some details

Now, we continue our tour through Beauville, Narasimhan, Ramanan. We’ve talked about Twisted Endomorphisms and we’ve talked about the Generalized Theta Divisor on the Moduli Space of Vector Bundles. So today we’ll talk a bit about Abelian Varieties, Principal Polarizations, … Continue reading

## Local Fields

Dear Readers, Let’s examine the role of topology in the study of fields and arithmetic. A topology on a field compatible with the field operations is given by an absolute value, which in turn defines a metric. Outside of number … Continue reading

Posted in Uncategorized
3 Comments