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This tag is used if a reference is needed in a paper or textbook on a specific result.

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Is there an english translation of Delignes "La conjecture de Weil pour les surfaces K3."?

Yes there is. Just google "deligne proof of weil conjecture for k3 surfaces" and click on the first (or second) link.
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8 votes
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Reference request: Diophantine equations

This may be a good choice for someone who (like yourself) is already superficially acquainted with some of the definitions and methods of Diophantine geometry: Marc Hindry, Joseph H. Silverman -- Dio …
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13 votes

Finding $q(x)$ such that $p(q(x))$ is reducible over $\mathbb{Q}[x]$

Note: in this answer, I have inadvertently disregarded your requirement for $q$ to have integral coefficients. I do however prove that a $q$ with rational coefficients does exist, so I will just let t …
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16 votes
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reference request: rational points on the unit sphere

The earliest reference is surely Diophantus' Arithmetica. His "method of adequality" can be used to construct rational points on quadrics that approximate real points arbitrarily well (that is, starti …
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8 votes

Textbook for Etale Cohomology

My first exposure to étale cohomology was through Bjorn Poonen's notes Rational Points on Varieties, Ch. 6. Not all of the big theorems are mentioned there, but it provides a great introduction to tho …
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2 votes

Rational solutions to $P(x,y)=0$ for $P$ reducible over ${\mathbb C}$

This also follows from Prop. 2.3.26(i) in Bjorn Poonen's Rational Points on Varieties, where it is stated that if for a finite type $k$-scheme $X$ the set of rational points $X(k)$ is Zariski dense, t …
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12 votes
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Galois groups of classical differential equations

I am currently on the lookout for good motivational examples for differential Galois theory, and I was wondering the following: Is there a book or article devoted (either partially or completely) to …
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3 votes

A road map through group cohomology

Chapter 2 of these notes by Milne have been helpful to me.
6 votes
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Reference request to proof that H$^2(\Gamma, \mathbb{Q}/\mathbb{Z}) = 0$

By the Galois cohomology long exact sequence, this is isomorphic to $\operatorname{H}^3(\Gamma,\mathbb{Z})$, and the vanishing of this is Chapter I, Corollary 4.17 in Milne's Arithmetic Duality Theore …
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2 votes

reference for (co)homology theories

I learned sheaf cohomology from Claire Voisin's Hodge Theory and Complex Algebraic Geometry I. This is a great book. As its name suggests, it also spends quite some time explaining Dolbeault cohomolog …
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3 votes
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What is the state-of-the-art for solving polynomials systems over fields that are not algebr...

For the reals, I particularly like the book by Sturmfels mentioned by Alexandre Eremenko. For the rational numbers, you can hardly do better than Bjorn Poonen's book Rational Points on Varieties, whic …
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