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2018 | OriginalPaper | Buchkapitel

9. Towards Higher Genus

verfasst von : Peter Roquette

Erschienen in: The Riemann Hypothesis in Characteristic p in Historical Perspective

Verlag: Springer International Publishing

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Abstract

As I have told in Sect. 6.​2 Hasse originally was interested in the estimate of solutions of diophantine congruences. It was Artin who in November of 1932, when Hasse was visiting Hamburg, told him that the estimating problem was pointing to the RHp. It appears that at that time Hasse did not yet believe in the general validity of the RHp for all function fields with higher genus g > 1. (See page 65.)

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Vorheriges Kapitel More on Elliptic Fields
Nächstes Kapitel A Virtual Proof
Fußnoten
1
In the summer term of 1933 Davenport stayed in Göttingen with a stipend he had got from his College. Thus he became a witness of the dissolution of the Göttingen mathematical scene due to the disastrous policy of the Nazi government. On weekends he often went to Marburg, which is not far from Göttingen, in order to meet Hasse. But sometimes there were letters exchanged.
 
2
It appears that Hasse had those automorphisms in mind which respect the “addition” of two point sets. He knew already from the elliptic case that there are more field automorphisms, namely the translations. See page 95.
 
3
President of the University.
 
4
The official organization of mathematics students which at that time was dominated by Nazi students.
 
5
An additional reason for removing Tornier from Göttingen may have been that he permanently produced financial trouble. He had pawned a large part of his future salary and also had asked for and received high sums from the university as advance payment. It appears that he had fallen back to his addiction to drugs (morphine) which Hasse had mentioned in a letter to Fraenkel of 10 July 1927. (At that time Hasse had believed that Tornier had been able to overcome this.) But at Berlin University Tornier did not stop this behavior and in 1938, when he was caught in financial fraud he had to leave the university and also the Nazi party. More precisely, in order to avoid public scandal he was “advised” to leave the party and the university on his own application. He then retreated to a psychiatric clinic in Silesia. These facts are documented in the personal files for Tornier at the archive of Humboldt University in Berlin.
 
6
That was what apparently many people at those times still expected or at least hoped. And not only at those times.
 
7
As to the terminology and the description of the situation see page 96 ff.
 
8
Among them was the work of Weil’s student Elizabeth Lutz at Strassbourg on the structure of the group of rational points of an elliptic curve over a \(\mathfrak {p}\)-adic field (\(\mathfrak {p}\)-adic uniformization). Weil had proposed to have Lutz’s paper published in Göttingen as a “sign of continued cooperation”. Hasse gladly agreed; he accepted Lutz’s paper for Crelle’s Journal [Lut37].
 
9
I have found this expression in Schappacher’s survey [Sch07].
 
10
Rohrbach had held a position at Berlin University but had got there into trouble because of political reasons.
 
11
She too came from Berlin. There she did not like the Nazi dominated atmosphere and therefore she had asked Rohrbach where to go for her Ph.D. Rohrbach suggested to come to Göttingen too and study with Hasse. The latter proposed to her to work on the foundation of arithmetics in higher dimensional function fields. But one year later von Caemmerer suddenly left Göttingen and went to Britain where she married Bernhard Neumann with whom she had been secretly engaged in Berlin already. He was Jewish and therefore had to leave Germany. Both Hanna and Bernhard grew to become well known group theorists.
 
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Metadaten
Titel
Towards Higher Genus
verfasst von
Peter Roquette
Copyright-Jahr
2018
Buch
The Riemann Hypothesis in Characteristic p in Historical Perspective

Print ISBN: 978-3-319-99066-8

Electronic ISBN: 978-3-319-99067-5

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-99067-5_9

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