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Field arithmetic / Michael D. Fried, Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden |
| Autore | Fried, Michael D. |
| Edizione | [4. ed] |
| Pubbl/distr/stampa | Cham, : Springer, 2023 |
| Descrizione fisica | xxxi, 827 p. : ill. ; 24 cm |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto topico |
12-XX - Field theory and polynomials [MSC 2020]
12E25 - Hilbertian fields; Hilbert's irreducibility theorem [MSC 2020] 12E30 - Field arithmetic [MSC 2020] 12F12 - Inverse Galois theory [MSC 2020] 12Lxx - Connections between field theory and logic [MSC 2020] 14G05 - Rational points [MSC 2020] |
| Soggetto non controllato |
Absolute Galois Groups
Algebra Algebraic Geometry Finite Groups Galois Groups Galois Stratification Galois theory Hilbertian Fields Irreducibility PAC Fields Profinite groups Ultraproducts |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00279430 |
Fried, Michael D.
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| Cham, : Springer, 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Field arithmetic / Michael D. Fried, Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden |
| Autore | Fried, Michael D. <1942- > |
| Pubbl/distr/stampa | Berlin, : Springer, 1986 |
| Descrizione fisica | xvi, 458 p. : ill. ; 25 cm |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto topico |
12-XX - Field theory and polynomials [MSC 2020]
14G05 - Rational points [MSC 2020] 12E25 - Hilbertian fields; Hilbert's irreducibility theorem [MSC 2020] 03C60 - Model-theoretic algebra [MSC 2020] 03H15 - Nonstandard models of arithmetic [MSC 2020] 03C20 - Ultraproducts and related constructions [MSC 2020] 12E30 - Field arithmetic [MSC 2020] 03C10 - Quantifier elimination, model completeness and related topics [MSC 2020] 12L12 - Model theory of fields [MSC 2020] 12L15 - Nonstandard arithmetic and field theory [MSC 2020] 12L05 - Decidability and field theory [MSC 2020] |
| Soggetto non controllato |
Absolute Galois Groups
Algebra Algebraic Geometry Finite Groups Galois Stratification Galois groups Galois theory Hilbertian Fields Irreducibility PAC Fields Profinite groups ultraproductS |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0263774 |
|
Fried, Michael D. <1942- >
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| Berlin, : Springer, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Field arithmetic / Michael D. Fried, Moshe Jarden
| Field arithmetic / Michael D. Fried, Moshe Jarden |
| Autore | Fried, Michael D. |
| Pubbl/distr/stampa | Berlin, : Springer, 1986 |
| Descrizione fisica | xvi, 458 p. : ill. ; 25 cm |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto topico |
03C10 - Quantifier elimination, model completeness and related topics [MSC 2020]
03C20 - Ultraproducts and related constructions [MSC 2020] 03C60 - Model-theoretic algebra [MSC 2020] 03H15 - Nonstandard models of arithmetic [MSC 2020] 12-XX - Field theory and polynomials [MSC 2020] 12E25 - Hilbertian fields; Hilbert's irreducibility theorem [MSC 2020] 12E30 - Field arithmetic [MSC 2020] 12L05 - Decidability and field theory [MSC 2020] 12L12 - Model theory of fields [MSC 2020] 12L15 - Nonstandard arithmetic and field theory [MSC 2020] 14G05 - Rational points [MSC 2020] |
| Soggetto non controllato |
Absolute Galois Groups
Algebra Algebraic Geometry Finite Groups Galois Groups Galois Stratification Galois theory Hilbertian Fields Irreducibility PAC Fields Profinite groups Ultraproducts |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? |
| Titolo uniforme | |
| Record Nr. | UNICAMPANIA-VAN00263774 |
|
Fried, Michael D.
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| Berlin, : Springer, 1986 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
The Absolute Galois Group of a Semi-Local Field / Dan Haran, Moshe Jarden
| The Absolute Galois Group of a Semi-Local Field / Dan Haran, Moshe Jarden |
| Autore | Haran, Dan |
| Pubbl/distr/stampa | Cham, : Springer, 2021 |
| Descrizione fisica | xvi, 137 p. : ill. ; 24 cm |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto topico |
12-XX - Field theory and polynomials [MSC 2020]
12F10 - Separable extensions, Galois theory [MSC 2020] 12E25 - Hilbertian fields; Hilbert's irreducibility theorem [MSC 2020] 12E30 - Field arithmetic [MSC 2020] |
| Soggetto non controllato |
Absolute Galois Groups
Embedding problem Field arithmetic Free profinite product of profinite group Haar measure Semi-local fields Strong projectivity |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0275333 |
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Haran, Dan
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||
| Cham, : Springer, 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
The Absolute Galois Group of a Semi-Local Field / Dan Haran, Moshe Jarden
| The Absolute Galois Group of a Semi-Local Field / Dan Haran, Moshe Jarden |
| Autore | Haran, Dan |
| Pubbl/distr/stampa | Cham, : Springer, 2021 |
| Descrizione fisica | xvi, 137 p. : ill. ; 24 cm |
| Altri autori (Persone) | Jarden, Moshe |
| Soggetto topico |
12-XX - Field theory and polynomials [MSC 2020]
12E25 - Hilbertian fields; Hilbert's irreducibility theorem [MSC 2020] 12E30 - Field arithmetic [MSC 2020] 12F10 - Separable extensions, Galois theory [MSC 2020] |
| Soggetto non controllato |
Absolute Galois Groups
Embedding Problem Field arithmetic Free profinite product of profinite group Haar measure Semi-local fields Strong projectivity |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00275333 |
|
Haran, Dan
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||
| Cham, : Springer, 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Valuations, orderings and Milnor K-theory / Ido Efrat
| Valuations, orderings and Milnor K-theory / Ido Efrat |
| Autore | Efrat, Ido |
| Pubbl/distr/stampa | Providence, : American mathematical society, 2006 |
| Descrizione fisica | XIII, 288 p. ; 26 cm. |
| Soggetto topico |
12J15 - Ordered fields [MSC 2020]
12J10 - Valued fields [MSC 2020] 12J20 - General valuation theory for fields [MSC 2020] 12E30 - Field arithmetic [MSC 2020] |
| ISBN | 08-218-4041-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-SUN0071778 |
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Efrat, Ido
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||
| Providence, : American mathematical society, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Valuations, orderings and Milnor K-theory / Ido Efrat
| Valuations, orderings and Milnor K-theory / Ido Efrat |
| Autore | Efrat, Ido |
| Pubbl/distr/stampa | Providence, : American mathematical society, 2006 |
| Descrizione fisica | XIII, 288 p. ; 26 cm. |
| Soggetto topico |
12J15 - Ordered fields [MSC 2020]
12J10 - Valued fields [MSC 2020] 12J20 - General valuation theory for fields [MSC 2020] 12E30 - Field arithmetic [MSC 2020] |
| ISBN | 08-218-4041-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISOB-VAN0071778 |
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Efrat, Ido
|
||
| Providence, : American mathematical society, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Suor Orsola Benincasa | ||
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Valuations, orderings and Milnor K-theory / Ido Efrat
| Valuations, orderings and Milnor K-theory / Ido Efrat |
| Autore | Efrat, Ido |
| Pubbl/distr/stampa | Providence, : American mathematical society, 2006 |
| Descrizione fisica | XIII, 288 p. ; 26 cm |
| Soggetto topico |
12J15 - Ordered fields [MSC 2020]
12J10 - Valued fields [MSC 2020] 12J20 - General valuation theory for fields [MSC 2020] 12E30 - Field arithmetic [MSC 2020] |
| ISBN | 978-08-218-4041-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0071778 |
|
Efrat, Ido
|
||
| Providence, : American mathematical society, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
Valuations, orderings and Milnor K-theory / Ido Efrat
| Valuations, orderings and Milnor K-theory / Ido Efrat |
| Autore | Efrat, Ido |
| Pubbl/distr/stampa | Providence, : American mathematical society, 2006 |
| Descrizione fisica | XIII, 288 p. ; 26 cm |
| Soggetto topico |
12E30 - Field arithmetic [MSC 2020]
12J10 - Valued fields [MSC 2020] 12J15 - Ordered fields [MSC 2020] 12J20 - General valuation theory for fields [MSC 2020] |
| ISBN | 978-08-218-4041-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN00071778 |
|
Efrat, Ido
|
||
| Providence, : American mathematical society, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
| ||
