@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-SKGJ9CKK-N
  skos:prefLabel "géométrie algébrique"@fr, "algebraic geometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-TCQHBZ3X-D .

psr:-NJ1RFLS0-8
  skos:prefLabel "ring theory"@en, "théorie des anneaux"@fr ;
  a skos:Concept ;
  skos:narrower psr:-TCQHBZ3X-D .

psr:-LMDZ11CG-L
  skos:prefLabel "algèbre homotopique"@fr, "homotopical algebra"@en ;
  a skos:Concept ;
  skos:narrower psr:-TCQHBZ3X-D .

psr: a skos:ConceptScheme .
psr:-TCQHBZ3X-D
  skos:broader psr:-LMDZ11CG-L, psr:-NJ1RFLS0-8, psr:-SKGJ9CKK-N ;
  dc:modified "2023-08-23"^^xsd:date ;
  dc:created "2023-08-23"^^xsd:date ;
  skos:prefLabel "géométrie algébrique dérivée"@fr, "derived algebraic geometry"@en ;
  skos:definition """<b>Derived algebraic geometry</b> is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathbb {Q} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">Q</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {Q} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="\\\\mathbb {Q} "></span>), simplicial commutative rings or <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E_{\\\\infty }}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msub>
<br/>          <mi>E</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </msub>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle E_{\\\\infty }}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68cacbe04c10fce753db60f346f92a34e1567d1e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:3.591ex; height:2.509ex;" alt="E_{{\\\\infty }}"></span>-ring spectra from algebraic topology, whose higher homotopy groups account for the non-discreteness (e.g., Tor) of the structure sheaf. Grothendieck's scheme theory allows the structure sheaf to carry nilpotent elements. Derived algebraic geometry can be thought of as an extension of this idea, and provides natural settings for intersection theory (or motivic homotopy theory) of singular algebraic varieties and cotangent complexes in deformation theory (cf. J. Francis), among the other applications. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Derived_algebraic_geometry">https://en.wikipedia.org/wiki/Derived_algebraic_geometry</a>)"""@en ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Derived_algebraic_geometry> .