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ETH Zürich

1. Wang, Ming-Xi. Rational points and transcendental points.

Degree: 2011, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/41776

Subjects/Keywords: ABELSCHE VARIETÄTEN + ABELSCHE SCHEMATA (ALGEBRAISCHE GEOMETRIE); ABELIAN VARIETIES + ABELIAN SCHEMES (ALGEBRAIC GEOMETRY); ELLIPTIC FUNCTIONS + ELLIPTIC INTEGRALS (MATHEMATICAL ANALYSIS); ALGEBRAIC CURVES (ALGEBRAIC GEOMETRY); ELLIPTISCHE FUNKTIONEN + ELLIPTISCHE INTEGRALE (ANALYSIS); ALGEBRAISCHE KURVEN (ALGEBRAISCHE GEOMETRIE); HOMOTOPY GROUPS + COHOMOTOPY GROUPS (ALGEBRAIC TOPOLOGY); HOMOTOPIEGRUPPEN + KOHOMOTOPIEGRUPPEN (ALGEBRAISCHE TOPOLOGIE); ENDOMORPHISM RINGS (ALGEBRA); ENDOMORPHISMENRINGE (ALGEBRA); info:eu-repo/classification/ddc/510; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Wang, M. (2011). Rational points and transcendental points. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/41776

Chicago Manual of Style (16^{th} Edition):

Wang, Ming-Xi. “Rational points and transcendental points.” 2011. Doctoral Dissertation, ETH Zürich. Accessed October 31, 2020. http://hdl.handle.net/20.500.11850/41776.

MLA Handbook (7^{th} Edition):

Wang, Ming-Xi. “Rational points and transcendental points.” 2011. Web. 31 Oct 2020.

Vancouver:

Wang M. Rational points and transcendental points. [Internet] [Doctoral dissertation]. ETH Zürich; 2011. [cited 2020 Oct 31]. Available from: http://hdl.handle.net/20.500.11850/41776.

Council of Science Editors:

Wang M. Rational points and transcendental points. [Doctoral Dissertation]. ETH Zürich; 2011. Available from: http://hdl.handle.net/20.500.11850/41776

Stellenbosch University

2.
Kriel, Marelize.
*Endomorphism**rings* of hyperelliptic Jacobians.

Degree: Mathematical Sciences, 2005, Stellenbosch University

URL: http://hdl.handle.net/10019.1/2874

Thesis (MSc (Mathematics)) – University of Stellenbosch, 2005.

The aim of this thesis is to study the unital subrings contained in associative algebras arising as the endomorphism algebras of hyperelliptic Jacobians over finite fields. In the first part we study associative algebras with special emphasis on maximal orders. In the second part we introduce the theory of abelian varieties over finite fields and study the ideal structures of their endomorphism rings. Finally we specialize to hyperelliptic Jacobians and study their endomorphism rings.

Subjects/Keywords: Mathematics; Associative algebras; Endomorphism rings; Jacobians; Abelian varieties

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Kriel, M. (2005). Endomorphism rings of hyperelliptic Jacobians. (Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/2874

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Kriel, Marelize. “Endomorphism rings of hyperelliptic Jacobians.” 2005. Thesis, Stellenbosch University. Accessed October 31, 2020. http://hdl.handle.net/10019.1/2874.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Kriel, Marelize. “Endomorphism rings of hyperelliptic Jacobians.” 2005. Web. 31 Oct 2020.

Vancouver:

Kriel M. Endomorphism rings of hyperelliptic Jacobians. [Internet] [Thesis]. Stellenbosch University; 2005. [cited 2020 Oct 31]. Available from: http://hdl.handle.net/10019.1/2874.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kriel M. Endomorphism rings of hyperelliptic Jacobians. [Thesis]. Stellenbosch University; 2005. Available from: http://hdl.handle.net/10019.1/2874

Not specified: Masters Thesis or Doctoral Dissertation

University of Kansas

3. Se, Tony. Depth and Associated Primes of Modules over a Ring.

Degree: PhD, Mathematics, 2016, University of Kansas

URL: http://hdl.handle.net/1808/21895

This thesis consists of three main topics. In the first topic, we let R be a commutative Noetherian ring, I,J ideals of R, M a finitely generated R-module and F an R-linear covariant functor. We ask whether the sets \operatorname{Ass}_{R} F(M/I^{n} M) and the values \operatorname{depth}_{J} F(M/I^{n} M) become independent of n for large n. In the second topic, we consider rings of the form R = k[x^{a},x^{p1}y^{q1}, …,x^{pt}y^{qt},y^{b}], where k is a field and x,y are indeterminates over k. We will try to formulate simple criteria to determine whether or not R is Cohen-Macaulay. Finally, in the third topic we introduce and study basic properties of two types of modules over a commutative Noetherian ring R of positive prime characteristic. The first is the category of modules of finite F-type. They include reflexive ideals representing torsion elements in the divisor class group. The second class is what we call F-abundant modules. These include, for example, the ring R itself and the canonical module when R has positive splitting dimension. We prove many facts about these two categories and how they are related. Our methods allow us to extend previous results by Patakfalvi-Schwede, Yao and Watanabe. They also afford a deeper understanding of these objects, including complete classifications in many cases of interest, such as complete intersections and invariant subrings.
*Advisors/Committee Members: Dao, Hailong (advisor), Jiang, Yunfeng (cmtemember), Katz, Daniel (cmtemember), Lang, Jeffrey (cmtemember), Nutting, Eileen (cmtemember).*

Subjects/Keywords: Mathematics; Cohen-Macaulay; coherent functors; divisor class group; F -regularity; Frobenius endomorphism; semigroup rings

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Se, T. (2016). Depth and Associated Primes of Modules over a Ring. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/21895

Chicago Manual of Style (16^{th} Edition):

Se, Tony. “Depth and Associated Primes of Modules over a Ring.” 2016. Doctoral Dissertation, University of Kansas. Accessed October 31, 2020. http://hdl.handle.net/1808/21895.

MLA Handbook (7^{th} Edition):

Se, Tony. “Depth and Associated Primes of Modules over a Ring.” 2016. Web. 31 Oct 2020.

Vancouver:

Se T. Depth and Associated Primes of Modules over a Ring. [Internet] [Doctoral dissertation]. University of Kansas; 2016. [cited 2020 Oct 31]. Available from: http://hdl.handle.net/1808/21895.

Council of Science Editors:

Se T. Depth and Associated Primes of Modules over a Ring. [Doctoral Dissertation]. University of Kansas; 2016. Available from: http://hdl.handle.net/1808/21895