Über die Picard'schen Gruppen aus dem Zahlkörper der dritten und der vierten…

(3 User reviews)   3276
By Charlotte Girard Posted on Nov 15, 2025
In Category - Philosophy
Bohler, Otto Bohler, Otto
German
Okay, I need to be honest right away—this isn't your typical bedtime read. 'Über die Picard'schen Gruppen...' by Otto Bohler is a deep, technical dive into a very specific corner of number theory. Think of it as a detective story, but the mystery is about mathematical structures called Picard groups within certain number fields. Bohler isn't chasing a criminal; he's chasing clarity and proof in a landscape of abstract algebra. The 'conflict' is the intellectual challenge itself: untangling complex relationships between these groups to reveal something new. If you love seeing how intricate mathematical puzzles are solved, this is a fascinating record of that process. It's a quiet, intense book written for a very specific audience.
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place of vantage. Amid a lull in their clamour the crier recommenced. “And now, men of Hellas, another time hearken. The sixth contestant in the pentathlon, most honourable of the games held at the Isthmus, is Glaucon, son of Conon the Athenian; his grandfather—” a jangling shout drowned him. “The most beautiful man in Hellas!” “But an effeminate puppy!” “Of the noble house of Alcmæon!” “The family’s accursed!” “A great god helps him—even Eros.” “Ay—the fool married for mere love. He needs help. His father disinherited him.” “Peace, peace,” urged the crier; “I’ll tell all about him, as I have of the others. Know then, my masters, that he loved, and won in marriage, Hermione, daughter of Hermippus of Eleusis. Now Hermippus is Conon’s mortal enemy; therefore in great wrath Conon disinherited his son,—but now, consenting to forgive him if he wins the parsley crown in the pentathlon—” “A safe promise,” interrupted a Spartan in broadest Doric; “the pretty boy has no chance against Lycon, our Laconian giant.” “Boaster!” retorted an Athenian. “Did not Glaucon bend open a horseshoe yesterday?” “Our Mœrocles did that,” called a Mantinean; whereupon the crier, foregoing his long speech on Glaucon’s noble ancestry, began to urge the Athenians to show their confidence by their wagers. “How much is staked that Glaucon can beat Ctesias of Epidaurus?” “We don’t match our lion against mice!” roared the noisiest Athenian. “Or Amyntas of Thebes?” “Not Amyntas! Give us Lycon of Sparta.” “Lycon let it be,—how much is staked and by whom, that Glaucon of Athens, contending for the first time in the great games, defeats Lycon of Sparta, twice victor at Nemea, once at Delphi, and once at Olympia?” The second rush and outcry put the crier nearly at his wits’ end to record the wagers that pelted him, and which testified how much confidence the numerous Athenians had in their unproved champion. The brawl of voices drew newcomers from far and near. The chariot race had just ended in the adjoining hippodrome; and the idle crowd, intent on a new excitement, came surging up like waves. In such a whirlpool of tossing arms and shoving elbows, he who was small of stature and short of breath stood a scanty chance of getting close enough to the crier’s stand to have his wager recorded. Such, at least, was the fate of a gray but dignified little man, who struggled vainly—even with risk to his long linen chiton—to reach the front. “Ugh! ugh! Make way, good people,—Zeus confound you, brute of a Spartan, your big sandals crush my toes again! Can I never get near enough to place my two minæ on that Glaucon?” “Keep back, graybeard,” snapped the Spartan; “thank the god if you can hold your money and not lose it, when Glaucon’s neck is wrung to-morrow.” Whereupon he lifted his own voice with, “Thirty drachmæ to place on Lycon, Master Crier! So you have it—” “And two minæ on Glaucon,” piped the little man, peering up with bright, beady eyes; but the crier would never have heard him, save for a sudden ally. “Who wants to stake on Glaucon?” burst in a hearty young Athenian who had wagered already. “You, worthy sir? Then by Athena’s owls they shall hear you! Lend us your elbow, Democrates.” The latter request was to a second young Athenian close by. With his stalwart helpers thrusting at either side, the little man was soon close to the crier. “Two minæ?” quoth the latter, leaning, “two that Glaucon beats Lycon, and at even odds? But your name, sir—” The little man straightened...

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Let's get this out in the open: this book is a specialized academic monograph. It's not a novel with characters or a plot in the traditional sense. The 'story' here is the logical argument and investigation.

The Story

Bohler focuses on a technical area of algebraic number theory. He examines properties of mathematical objects called Picard groups (which relate to how numbers factor in certain settings) within number fields of degrees three and four. The 'narrative' is his methodical exploration: setting up the problem, applying tools from class field theory and group theory, and working through the calculations and proofs to establish his results. It's a journey from a posed question to a concluded answer, built entirely on logic and precision.

Why You Should Read It

You shouldn't, unless this is your field. And if it is your field, you probably already know about it! For a graduate student or researcher in algebraic number theory, Bohler's work represents a clear, dedicated treatment of a niche topic. The value is in its rigor and focus. It's like a master craftsman's notebook—not for entertainment, but for reference and insight into a particular technique. There's a certain beauty in that kind of dedicated, pure inquiry, even if it's inaccessible to most.

Final Verdict

This book is for a razor-thin audience: specialists in algebraic number theory, particularly those working on class groups or Picard groups. It's a resource, not recreational reading. For the general book lover, it's impenetrable. But for that right reader, it's a serious and useful piece of the mathematical literature. Think of it as a highly advanced tool—incredibly valuable for the specific job it was designed for.



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Charles Harris
1 year ago

A bit long but worth it.

Sarah Perez
1 month ago

I was skeptical at first, but the character development leaves a lasting impact. Don't hesitate to start reading.

George Martin
7 months ago

Wow.

5
5 out of 5 (3 User reviews )

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