Modern Algebraic Geometry and Analytic Number TheoryModern algebraic geometry vs. classical algebraic...
Modern Algebraic Geometry and Analytic Number Theory
Modern algebraic geometry vs. classical algebraic geometryAnalytic tools in algebraic geometry Stacks in modern number theory/arithmetic geometryAsymptotic formula in Analytic Number TheorySpinoffs of analytic number theoryIntroductions to modern algebraic geometryHow much of modern algebraic geometry is there in modern complex(algebraic, analytic, differential) geometry?Algebraic Geometry in Number TheoryComplex analytic vs algebraic geometryMotivation behind Analytic Number Theory
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I am currently discovering the algebraic geometry of Grothendieck. I have the impression that this theory, which leads to categories, schemas, topos etc. alone can encompass all modern mathematics (with the exception of probabilities). That is to say, to understand it, you really need to know everything. It also has extraordinary opportunities in the understanding of arithmetic (Pierre Deligne in the proofs of André Weil etc.).
However, I don't see any connection with the analytic number theory like the one undertaken by Dirichlet, Von Mangoldt, Chebyshev, Hardy, Littlewood, Ramanujan, and so on.
Does anyone have ideas of theorems, conjectures, or "approaches" that
combine these two points of view?
ag.algebraic-geometry at.algebraic-topology analytic-number-theory dirichlet-series
edited 1 hour ago
Francesco Polizzi
48k3127207
asked 1 hour ago
lulu2612lulu2612
183
$endgroup$
add a comment |
$begingroup$
I am currently discovering the algebraic geometry of Grothendieck. I have the impression that this theory, which leads to categories, schemas, topos etc. alone can encompass all modern mathematics (with the exception of probabilities). That is to say, to understand it, you really need to know everything. It also has extraordinary opportunities in the understanding of arithmetic (Pierre Deligne in the proofs of André Weil etc.).
However, I don't see any connection with the analytic number theory like the one undertaken by Dirichlet, Von Mangoldt, Chebyshev, Hardy, Littlewood, Ramanujan, and so on.
Does anyone have ideas of theorems, conjectures, or "approaches" that
combine these two points of view?
ag.algebraic-geometry at.algebraic-topology analytic-number-theory dirichlet-series
edited 1 hour ago
Francesco Polizzi
48k3127207
asked 1 hour ago
lulu2612lulu2612
183
$endgroup$
7
$begingroup$
I like the question at the end of your post, but I think that your claim "encompass all modern mathematics" is quite exaggerated.
$endgroup$
– EFinat-S
1 hour ago
add a comment |
$begingroup$
I am currently discovering the algebraic geometry of Grothendieck. I have the impression that this theory, which leads to categories, schemas, topos etc. alone can encompass all modern mathematics (with the exception of probabilities). That is to say, to understand it, you really need to know everything. It also has extraordinary opportunities in the understanding of arithmetic (Pierre Deligne in the proofs of André Weil etc.).
However, I don't see any connection with the analytic number theory like the one undertaken by Dirichlet, Von Mangoldt, Chebyshev, Hardy, Littlewood, Ramanujan, and so on.
Does anyone have ideas of theorems, conjectures, or "approaches" that
combine these two points of view?
ag.algebraic-geometry at.algebraic-topology analytic-number-theory dirichlet-series
edited 1 hour ago
Francesco Polizzi
48k3127207
asked 1 hour ago
lulu2612lulu2612
183
$endgroup$
I am currently discovering the algebraic geometry of Grothendieck. I have the impression that this theory, which leads to categories, schemas, topos etc. alone can encompass all modern mathematics (with the exception of probabilities). That is to say, to understand it, you really need to know everything. It also has extraordinary opportunities in the understanding of arithmetic (Pierre Deligne in the proofs of André Weil etc.).
However, I don't see any connection with the analytic number theory like the one undertaken by Dirichlet, Von Mangoldt, Chebyshev, Hardy, Littlewood, Ramanujan, and so on.
Does anyone have ideas of theorems, conjectures, or "approaches" that
combine these two points of view?
ag.algebraic-geometry at.algebraic-topology analytic-number-theory dirichlet-series
ag.algebraic-geometry at.algebraic-topology analytic-number-theory dirichlet-series
edited 1 hour ago
Francesco Polizzi
48k3127207
asked 1 hour ago
lulu2612lulu2612
183
edited 1 hour ago
Francesco Polizzi
48k3127207
asked 1 hour ago
lulu2612lulu2612
183
edited 1 hour ago
Francesco Polizzi
48k3127207
edited 1 hour ago
Francesco Polizzi
48k3127207
edited 1 hour ago
Francesco Polizzi
48k3127207
48k3127207
asked 1 hour ago
lulu2612lulu2612
183
asked 1 hour ago
lulu2612lulu2612
183
asked 1 hour ago
lulu2612lulu2612
183
183
7
$begingroup$
I like the question at the end of your post, but I think that your claim "encompass all modern mathematics" is quite exaggerated.
$endgroup$
– EFinat-S
1 hour ago
add a comment |
7
$begingroup$
I like the question at the end of your post, but I think that your claim "encompass all modern mathematics" is quite exaggerated.
$endgroup$
– EFinat-S
1 hour ago
7
7
$begingroup$
I like the question at the end of your post, but I think that your claim "encompass all modern mathematics" is quite exaggerated.
$endgroup$
– EFinat-S
1 hour ago
$begingroup$
I like the question at the end of your post, but I think that your claim "encompass all modern mathematics" is quite exaggerated.
$endgroup$
– EFinat-S
1 hour ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
There are lots of examples, so let me just tell one.
P. Deligne (1971) used Eichler–Shimura isomorphism to reduce the Ramanujan conjecture on the $tau$ function to the Weil conjectures, that he later proved by using the full strength of Grothendieck's machinery.
answered 1 hour ago
Francesco PolizziFrancesco Polizzi
48k3127207
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
There are lots of examples, so let me just tell one.
P. Deligne (1971) used Eichler–Shimura isomorphism to reduce the Ramanujan conjecture on the $tau$ function to the Weil conjectures, that he later proved by using the full strength of Grothendieck's machinery.
answered 1 hour ago
Francesco PolizziFrancesco Polizzi
48k3127207
$endgroup$
add a comment |
$begingroup$
There are lots of examples, so let me just tell one.
P. Deligne (1971) used Eichler–Shimura isomorphism to reduce the Ramanujan conjecture on the $tau$ function to the Weil conjectures, that he later proved by using the full strength of Grothendieck's machinery.
answered 1 hour ago
Francesco PolizziFrancesco Polizzi
48k3127207
$endgroup$
add a comment |
$begingroup$
There are lots of examples, so let me just tell one.
P. Deligne (1971) used Eichler–Shimura isomorphism to reduce the Ramanujan conjecture on the $tau$ function to the Weil conjectures, that he later proved by using the full strength of Grothendieck's machinery.
answered 1 hour ago
Francesco PolizziFrancesco Polizzi
48k3127207
$endgroup$
There are lots of examples, so let me just tell one.
P. Deligne (1971) used Eichler–Shimura isomorphism to reduce the Ramanujan conjecture on the $tau$ function to the Weil conjectures, that he later proved by using the full strength of Grothendieck's machinery.
answered 1 hour ago
Francesco PolizziFrancesco Polizzi
48k3127207
edited 1 hour ago
answered 1 hour ago
Francesco PolizziFrancesco Polizzi
48k3127207
answered 1 hour ago
Francesco PolizziFrancesco Polizzi
48k3127207
answered 1 hour ago
Francesco PolizziFrancesco Polizzi
48k3127207
48k3127207
add a comment |
add a comment |
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7
$begingroup$
I like the question at the end of your post, but I think that your claim "encompass all modern mathematics" is quite exaggerated.
$endgroup$
– EFinat-S
1 hour ago